This article is from the Computer Viruses FAQ, by Nick FitzGerald n.fitzgerald@csc.canterbury.ac.nz with numerous contributions by others.
Assuming that you did not boot or run any executable programs from the
infected disk, the answer generally is no. There are two caveats:
1. You should be somewhat concerned about checking the integrity
of these data files as they may have been destroyed or
altered by the virus.
2. If any of the "data" files are interpretable as executable by
some other program (such as a Lotus macro) then these files
should be treated as potentially malicious until the symptoms
of the infection are known.
The copying process itself is safe (given the above scenario) although
you should be concerned with what type of files are being copied to
avoid introducing other problems.
 
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