Yes, FM Server can do it.
Please pay attention to where you put the file to import. Server side Imports only works into specific default folders
Does anyone know which default folders work?
See this knowledgebase article: http://help.filemaker.com/app/answers/detail/a_id/7035/kw/server%20import%20records
You might also take a closer look at your data. If you can reduce the number of indexed fields and the number of stored calculation fields, your data will import more quickly. But make such changes carefull, changing the storage options on a field can affect database performance, so you might get a faster import, but a slower performing database if you aren't careful.