No, because the Prime Directive didn't apply to that situation.
First, let's look at what the Prime Directive is. (All quotes from the linked Memory Alpha page.)
The Prime Directive, also known as Starfleet General Order 1 or the Non-Interference Directive, was the embodiment of one of Starfleet's most important ethical principles: noninterference with other cultures and civilizations. At its core was the philosophical concept that covered personnel should refrain from interfering in the natural, unassisted, development of societies, even if such interference was well-intentioned.
A complicated order, the Prime Directive had 47 sub-orders by the latter part of the 24th century. However, a high-level summary was "no identification of self or mission; no interference with the social development of said planet; no references to space, other worlds, or advanced civilizations."
There are two important bits to note here. First, is that the rule is about societies and cultures; it doesn't directly cover contact with non-sapient lifeforms. Second, it largely concerns hiding the existence of alien life from a developing planet; Starfleet commanders are generally a lot less concerned with the directive when the group in question already possesses "advanced" knowledge.
Now, let's look at what the Prime Directive is not.
The Prime Directive did not apply equally to all societies on all planets at all times. Although a cornerstone of Federation philosophy, the scope of the Prime Directive varied depending on many factors. For example, the Prime Directive primarily applied to societies that had little to no actual knowledge of other worlds and space-faring civilizations (as with certain pre-warp civilizations). [...] Human colonies were excluded from its coverage all together, and by virtue of joining the United Federation of Planets member planets were subject to its laws, regulations, and authority. [...] The result was a spectrum of application: the more closely a civilization was tied to the Federation or Earth the greater the amount of interference in that civilization that was tolerated within the Prime Directive.
If a decision was made by the commanding officer that could potentially be a violation of the Prime Directive, the conclusions and rationale would need to be recorded and justified to Starfleet through the ship's or station's logs. [...] There were many exceptions [...] each was driven by the context of the situation, the society, and the circumstances at the moment.
These exceptions generally fell into the following categories:
- The society already knew of and contacted the Federation.
- The society hails or attacks a Federation vessel.
- The society is in diplomatic discussions with the Federation.
- The society was previously interfered with by Federation citizens, whether or not in violation of the Prime Directive (e.g., prior to the Prime Directive being in force; accidental interference).
Again, we see the directive mainly applies to pre-warp civilizations with no prior knowledge of alien beings. Also, we see that civilizations more closely connected to Earth and/or the Federation are increasingly more exempt from the directive.
So what happens in Demons?
- Crew has an emergency.
- Crew lands on a presumably-lifeless planet.
- Due to technobabble substance on the planet, clones of two crew members are created by accident.
- Both clones have full awareness of the original members' thoughts and memories.
- The clones are linked in some kind of hive awareness, but they/it seem to possess at least human sapience, although they are still a bit confused and disoriented by their new life.
How does the Prime Directive apply to Demons?
There was arguably no life on the planet before the crew arrived. There was certainly no remotely-intelligent life, nor was there any type of culture or civilization. Therefore the Prime Directive was inapplicable. (Of note, I remember an episode in TNG where colonizing planets with any existing life was forbidden, but I'm fairly confident that was outside the Prime Directive proper.)
Then, the crew members' contact with the mystery substance (the "Silver Blood") caused them to be cloned. This could constitute "accidental interference", but because the "interference" was with natural phenomena, not a culture, the situation is much more akin to the Riker incident. In essence, the clones are just a tech malfunction, and are therefore some kind of modified or engineered humans.
So we have a couple of basically-human clones. Clearly, they have a right to live and so forth. But they also have full knowledge of the Federation, warp technology, Federation principles and philosophy, etc. They are nearly indistinguishable from actual Federation officers, and by all rights are Federation citizens.
However, the "technology" used to create the clones means they're a bit alien still. The hive mind, and their general physiology, leave them unable to comfortably survive on the Voyager (if at all), plus they have some kind of natural affinity for the planet. Even if they could leave, they'd prefer to stay.
The Prime Directive doesn't apply to Federation officers, nearly-human settlers (ultimately) from Earth, or an entire culture that was not only created by the Federation, but has intimate connection to the Federation. It also doesn't apply to a culture who is currently attacking a Federation starship as a means of starting diplomatic discussions in relation to previous, accidental interference by the Federation.
By giving the newly-formed entity access to Federation DNA, memories, and technology1, Janeway isn't interfering with an undeveloped civilization; she's helping Federation citizens maintain the standard of living they're accustomed to.
1I'm not sure this last part is true. I just watched the last 10 minutes of the episode, and, other than clothing, there's no obvious technology sitting on the planet at the end.