Not simply. Unlike some pure-Perl modules, the DBD::SQLite distribution includes a number of C files that must be compiled. (This includes the code for the SQLite database itself.)

If you know exactly what type of server you're running on, and can get access to another machine of a similar type, you might be able to compile it there and then FTP the binary up to the web server, but there are so many variables involved that I would not recommend this unless you are extremely comfortable with C compilation.