Probably not. Let us take the case US v. Lowe where the evidence seems even more damning. Lowe was convicted, because his computer actually did contain hundreds of child porn images. Police had IP logs that indicated that someone at Lowe's address was hosting a porn-sharing network and they downloaded some porn from the network. After a raid, illegal images were found on one computer, and forensic evidence provided a bit of evidence regarding when some of the files were downloaded, which was also connected with a person opening an invoice file containing the defendant's address 40 minutes before one of the porn files finished downloading.
Lowe moved for acquittal and did not enter any evidence. The court denied the motion. Even so, the court commented that
I have to say, in this case, it has been particularly
difficult, even though it’s my job to do so, to discern
where that line [between speculation and reasonable inference]
is and where what might be a reasonable inference that can
be drawn from the record evidence becomes nothing more than an
invitation for the jury to speculate as to what the evidence may be or
what it may show
Lowe was convicted. On appeal, the court concluded that
no rational juror could find him guilty beyond a reasonable
doubt based on the evidence presented at trial.
A juror could conclude that there was porn on the computer and that the defendant occasionally used the computer. But
without improperly stacking inferences, no juror could infer
from such limited evidence of ownership and use that James
knowingly downloaded, possessed, and distributed the child
pornography found on the laptop.
The court noted that there were two other individuals in the house who also had access to the computer. In particular, no evidence was presented to prove that defendant's wife had not accessed the computer at the relevant time. There is a long list of things that the prosecution failed to prove (e.g. they provided no evidence regarding what the defendand and wife did for a living, which was relevant to the evidence regarding "opening an invoice". The court sums up by saying
the evidence presented here fell well short of what we have
found sufficient to convict in other cases involving multiple
possible users of a single device.
(Citations include US v. Oufnac, 449 F. App’x 472; US v. Mellies, 329 F. App’x 592. The court also found that
the evidence did not permit a juror to conclude that James
knew the HP Pavilion laptop contained child-pornography files
and permitted them to remain on the computer.
since the files were buried in a Shareaza file-sharing library, and no evidence was introduced to prove that the defendant had opened the file-sharing program.
If you apply the findings in this case to your hypothetical, you could not possibly get a conviction that would not be overturned by a reasonable appeals court. The details of Lowe's trial are not clear from the appeal, but it appears that Lowe (or his attorney, if there was one) failed to create doubt regarding the government's case. Legally speaking, the defendant is not required to create doubt, but the instruction on reasonable doubt may have contributed to the problem. The jury is told that "Possible doubts or doubts based purely on speculation are not reasonable doubts", but since there was porn on the computer, a juror would have had to speculate that someone else downloaded it. The jury is told that "it may arise from the evidence, the lack of evidence, or the nature of the evidence". We do not know to what extent defense failed to make the argument that the government's evidence was severely lacking.