Short answer: No.
Rationalization: In Lonely Among Us the energy field messed with the transporter system, allowing them to bring back Picard. (Translation: The transporters were exposed to the rare element of plotonium, allowing them to do what the plot needed.)
I'm going to my source for this, one I've cited here before, the Star Trek: The Next Generation Writers' Technical Manual, Fourth Season Edition. This was sent to me directly, in a pitch package by the ST:TNG Script Supervisor Lolita Fatjo, when I was invited in to pitch story ideas to the producers. This is one of the Writers' Guides sent to those who would be writing for the show and, in some ways, goes beyond canon because it defines canon. In other words, it tells the writers what they can and cannot do on screen.
On page 28, under The Transporter - Once and for All:
... The stream of molecules read by the pads is sent to the Pattern Buffer, a large cylindrical tank surrounded by superconducting electromagnetic coils. It is here that the object to be transported is stored momentarily before actual beaming away from the ship (or even within the ship). It is the Pattern Buffer and its associated subsystems that have been improved the most in the last half-century. While the actual molecules of an object are held in a spinning magnetic suspension (eight minutes before degradation), the construction sequence of the object can be read, recorded in computer memory (in some cases), and reproduced. There are limits to the complexity of the object, however, and this is where the potential "miracle" machine still eludes.
The Transporter cannot produce working duplicate copies of living tissue or organ systems.
The reason for this is that routine transport involves handling the incredibly vast amount of information required to "disassemble" and :reassemble" a human being or other life form. To transport something, the system must scan, process, and transmit this pattern information. This is analogous to a television, which serves as a conduit to the vast amount of visual information in a normal television transmission.
And from a little later:
Storing that information, however, is another matter. In our analogy, it would be like comparing a television (which is incapable of storing an image) to a videocassette recorder, which can store a relatively low-resolution recording of a television program. In order to store the patterns for a human being, one would have to record not only all the atomic and molecular configurations, but all the quantum and energy states of all the electron shells, and the brownian motions of every sub-atomic partical of every atom. While we cannot store all of this incredibly complex information, we can use it as it is being handled in real time.
(I've seen this with computer data in some programs I've had to write. Data came in so cast I could filter and pull what I needed, but I couldn't store it all (without filling my hard drive up).)
Also, more specifically addressing this, on page 12, it says:
Objects stored in computer memory have only a limited "resolution" so that one CANNOT store and reproduce a living being.
While Data is more object than living being, the complexity of a brain that stores a self-aware object would be more complex a pattern than the Enterprise computer could easily store without using vast amounts of memory -- which weren't available. (And there was no reason to assume they would need to restore Data before he transported.)
Also, on page 29:
One amazing exception to this process was witnessed in the episode Lonely Among Us, in which a slightly altered Captain Picard returned through the transporter; this can be assumed to have been a case of the transporter being affected by the electromagnetic forces of the cloud-entity (ah ha!).
(Yes, even the "ah ha!" is in the manual.)
So, no, Data could not have been restored from a transport buffer.