First larger wheels will not make you noticeably faster. They may reduce your rolling resistance a small amount which will help but you can get most/all of that advantage by putting similar tires on you 26" wheels. You will increase the gear ratios off all your gears but unless you don't currently have a high enough gear you will just end up using a lower gear than before.
Second if you are using rim brakes brakes may be a major problem. Brake calipers have a limited range of adjustment so even if you can mount the caliper brakes to your bike you may not be able to adjust them to you new rims. There are at least 5 different caliper lengths from short reach racing brakes to x-long reach BMX and walmart MTB calipers. The 3 sizes in between are often very hard to find.
Third as you noted rear hub spacing and chain line might be a problem. Road bikes and MTBs have different spacing and chain lines. This can probably be adjusted for by using the middle chain ring and spacing the new wheel to line it up.

This sounds like a project with lots of problems and little gain, but it might be possible to make it work.

Craig