NO. It is unlikely the Tyrannid menace were created by Human technology since they show up on the galactic map at the very edge of the Galaxy, far beyond the range of any Human technology has ever reached.
Their flight path indicates they are coming from outside the galaxy, not from within.
The genetic technology of the Tyrannids is FAR beyond anything created by Humanity, able to absorb and utilize the beneficial genetic templates of every species they absorb.
The Tyranids are an extragalactic composite species of hideous xenos that is actually a space-faring ecosystem comprised of innumerable different bioforms which are all variations on the same genetic theme. The Tyranid race is ultimately dedicated solely to its own survival, propagation and evolutionary advancement. The Tyranids collectively form a monstrous superorganism that travels across the universe in their great Hive Fleets of biomechanical Hive Ships, systematically consuming all other biomatter to enable its own rapid evolution and reproduction. All Tyranid organisms are synaptic (psychically-reactive), and each Tyranid creature within a Hive Fleet shares and contributes to a communal Hive Mind, which allows the trillions of beings comprising the Tyranid Hive Fleets to communicate and organise instantaneously on a staggering scale. Warhammer 40K Wiki -> Tyrannids
The first recorded contact between the Imperium and the Tyranids places their appearance in the Eastern Fringes of the galaxy in 745.M41. (the 41st Millenium). However, it is rumoured that the Ordo Xenos of the Inquisition had identified possible appearances of this xenos species as far back as the 35th Millennium.
These early incursions were likely to be "sleeper" genestealer incursions where they are able to mimic the appearance of an alien race while they slowly take over the species from within.
The xenos emerged from the intergalactic space of the Local Group of galaxies, their Hive Mind drawn to the Milky Way by the psychic beacon of the Astronomican transmitted by the Emperor's presence in the Warp from Terra. The first officially recorded contact with the Tyranids for the Imperium of Man came during a Tyranid attack on an Ocean World called Tyran, and from there Hive Fleet Behemoth continued directly towards the center of the galaxy, consuming all the worlds in its path. The Tyranids were defeated, barely, by the efforts of the Ultramarines Chapter of the Space Marines during the Battle of Macragge, although the Ultramarines suffered devastating losses that would take centuries to replace.
Judging from all of the varied incursions of Tyrannids simultaneously across the galaxy, each with a unique signature and genetic behavior.
The other aspect which would make this idea completely incomprehensible is the numbers of Tyrannid in each fleet. Though Humanity has tens of trillions of members scattered across the galaxy, each Tyrannid fleet has an uncountable number of members, absorbed from entire galaxies of the Local Group before their arrival in the Milky Way.
The Tyrannid menace was attracted by the Astronomican, the psychic navigation beacon of the near-dead God Emperor of Man. It resembled their own psychic potential used to travel at faster than light speeds.
A fully mobilized Tyranid Hive Fleet strikes shock, awe, and terror into even the most stalwart of humanity's defenders. Even when the xenos threat is eliminated (at great cost), it will not be long before another Tyranid migration emerges to take advantage of the situation. This is what makes the Tyranid species such a threat: it is an evolved meta-predator capable of out-producing, out-consuming, and out-lasting all other species it encounters, having done so on a disquietingly unknowable number of prior occasions across a vast swathe of intergalactic space.
As for the source of the rumor the Tyrannid were created by Human members of the Imperium, I would place that rumor as part of the campaign of the Tyrannid themselves.
What a better way to undermine a species than to tell them, their protectors are the originators of a terrible plague and as such shouldn't be trusted to rescue them from the potential xeno-biological threat.
By the time they Humans realize they have been infested, it is too late to rescue the general population. Then the Imperium is left to perform an Exterminatus, destroying all life on the planet. A complete loss for the Imperium and an inconvenience for the Tyrannid.
This image shows the multiple points of entry of disparate Tyrannid Fleets, each attacking in multiple pathways, attacking multiple worlds with millions upon millions of members in each subfleet.
