While a study of one subject is not a valid scientific experiment (and fundamentally before everything else I'm a scientist) here are my observations of the belt vs beltless perspective based only on my experience over the last 2 years of my training.
I stopped testing my 1RM beltless in 2007 and at the time i think the best squat I hit beltless was 150 with a belted max around 165kg
At the start of 2008 I gave myself a hernia deadlifting 200kg when i probably should have known better and ended up taking almost 6 months of training because i couldn't get it fixed until i had a quiet period at work in april 08.
After recovering from the surgery I had to start squatting again almost from scratch, in my first session i did 2x5 with 40kg and couldn't walk the next day. By the end of 2008 I was up to 177kg squat (belted) and I used a belt on anything above about 140 and would even use a belt when doing longer work sets at anything 70% or above. During this period i was using a relatively thin belt.
In 2009 I got serious about competing in strongman and realising that a lack of basic strength was a big problem for me set out to build up my squat, DL, MP and BP. I bought the thickest, stiffest, widest belt i could find (inzer 13mm lever belt) and started squatting and pulling. By June my squat was up to 200kg (belted)
I've done several different squat programs this year including wendlers 5/3/1 and a smolov cycle most recently. In each case I warmed up without the belt but put it on for all work sets including during the smolov program the higher rep sets of 9 and 7 reps at 70 and 75% and I can guarantee that I never did anything heavier than 150 without a belt!
End result - this year my belted back squat has gone from 177 to 208kg a 31kg improvement and my deadlift has gone from 215kg to 253kg (38kg) until last wednesday I had no idea what my unbelted squat was and didn't really care but this thread made me curious to see what the carry over from improving my belted squat was .
results of 1RM test beltless and belted below
http://www.youtube.com/watch?v=4Z4oxycJS_g