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Let's say you had a BOA CC with $8000 limit and a $1600 cash advance limit. BOA sent you convenience checks. Are you able to write a convenience check up till your $8k limit or would you be limited to your $1.6k cash advance limit?
Chances are that you'll be limited to your cash advance limit. Also, hopefully those convenience checks have some promo like 3% fee for a year at no interest or something, since immediately accruing interest at 20% or so won't be fun.
My wife and I both get these checks from BOA every month and my personal experience is that the convenience checks are not limited to your cash advance limit. I think they are considered more a balance transfer than a cash advance, although they do incur a higher interest rate after the promo period.
In any case, if you are unsure, you can always call.