Would purchasing the full verion allow me to view the data in the cyrillic font it was created in originally?
No - there are no additional features in the full version. You could try modifying the converted file to use a compatible font - IF a compatible font can be found.
The issue (or rather, one of the issues) here is that Filemaker switched to Unicode in version 7. Previous versions use a different type of encoding. This is further complicated by the fact that the encoding is different for Windows and Macintosh platforms - so Windows users may see "garbage" in a file sent to them by a Mac user, even if they are all using the same (pre-7) version of Filemaker.
I think your best bet would be to ask the author to send you the data as a Unicode text file, which you can then import to the converted solution.