I wouldn't think so. When I upload photos from my digital camera to print through Walgreens, it typically doesn't give me a resolution warning message at any size, not even at 20" x 30" (though I've never actually printed that large).
This picture isn't 12x12, but it's big. I actually printed one bigger, but I couldn't do the borders the way I wanted. Anyway, this is scanned in 600dpi from an old 3x5 film print, so it wasn't great quality to begin with, but the enlargment printed out great. (I also printed out the plaid background.)
One problem for a background is that most photos aren't square, so you'll have to do some cropping. I've done it before, but I gave the album to my granddaughter and haven't gotten around to taking pictures...but it works good. I like to soften it some so it's more of a background than the star of the show. Then maybe have a small picture somewhere in the LO...if you're using multiple pics.
I print my customized stuff at home on my wide format printer. When I get an inspiration, I don't want to have to go to a store to pick it up.~Judy
I also use Costco for large prints. Usually I print 8x12 so I can still see some patterned paper or cardstock, but their 12x12's come out very nice too. I have never had a resolution problem, but I shoot with a DSLR in RAW, my files and resolution are large.