Are you downloading the correct patch (Max / Max Design)? They won't install on the wrong version. There are also separate 32bit and 64bit updates.
As for the installation folder, no it shouldn't make any difference. I have both the 32 and 64 bit versions installed, both in (different) folders directly off the root of the drive and they both work fine (and are fully patched).
Max 2016 (SP1/EXT1)
Win7Pro x64 (SP1). i5-3570K @ 4.4GHz, 8Gb Ram, DX11.
nVidia GTX760 (2GB) (Driver 430.86).