Certainly, you'd get a textured 'look' by leaving the glue on the wall. At the same time, this look may look like, well, glue that's been painted over.
What you might want to consider is trying DIF. It's made by Zinsser. (Click on Products to find it.) It's very inexpensive. Before you buy it, measure the amount of wall space in sq. ft.. You'll need to know how much to buy, and buy a little extra in case you want to wash the walls a 2nd time for what's left over. DO follow the directions TO THE 'T'. If you don't, you won't get the walls as clean as you like. (And your 'mistakes' will show up when you finally paint!) I use a big sponge, kinda like the ones you use to wash your car. Buy yourself a pair of rubber gloves so you don't burn your hands in the hot water. DIF is an enzyme that 'eats' at the glue to soften it up. Change the solution on a 'regular basis' per the instructions.
There is a home made solution but the 'mix' escapes me at the moment. It's a vinigar-based mixture. I don't know how good it is but the DIF is excellent! After you finished, buy yourself HIGH quality primer and paint from a PAINT RETAILER. (THey're found in the Yellow Pages under PAINT - RETAIL. Sherwin Williams, Finneran & Haley, etc., etc..) Others on the Forum may say more.