Yes, if an operator is willing to go to the effort. 

Publicizing your effort in advance via email is a good idea. Also involve other hams who are typically FM anchored so they can see the CW/SSB side of contesting; if they catch the contest bug they'll tell other FMers. A voice keyer on the FM stations is probably worthwhile as well.

One thing you'll run into is the FM station causing a bit of desense on the weak signal rig...unless you use one radio for both FM & CW/SSB.