no, 32-bit recognizes 4GB's max, but will only be able to use around 3, 3.5GB on average... basically you have to deduct the total amount of other Memory used in the system (except Hard drive storage etc), add up all the extra memory like Video card RAM, BIOS, CPU Cache, Cache from Hard drives & CD/DVD Drives, if you have one of those X-fi sound cards with RAM on it, that too, anything like that, add that together, subtract it from the 4GB max & that should/would be the amount that windows 32-bit will be able to use... so if for example you had 2 vid cards each with 1GB of RAM, right there, thats 2GB's, & you'll be left with just under 2GB's of RAM to use... (factoring in the small remaining bits else where in the system)
but thats mainly why many mention to go with a 64-bit OS... for example if you were to run 2 HD4870x2's with 2GB each, right there, thats your 4GB total, or at least should be... so would/should almost require you to go 64-bit OS.