Or was it the chicken before the egg? Who knows.
All kidding aside, yeah send them in. There are maaany places who are hurting so bad they'll take straight CFI's with no DG and get their CFII/MEI and checkouts. Sure it's hard to find one who'll pay for your II/MEI...but the point is with all three you should have no problem finding a place to work. I've flown into airports and just happened by the flight school for charts, drink, or what not and the second they find out your an instructor they ask if your interested in helping them out. Not sure where your from, but up here in NY we are hurting bad.