Won't the destination have to have an IAP too?
Destination
alternate (or destination itself if no alternate planned) must have a non-RNAV instrument approach available if an RNAV approach is intended at destination. So to answer your question, not necessarily.
For example... flew into Bordeaux not too long ago and they were on 05 with the VOR u/s. Available approaches were RNAV or visual. Alternate was La Rochelle, with ILS available - so both ok.