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.