I have an old smartphone so doubt it has an "internal pressure sensor", as far as I'm aware it uses gps to calculate your height. The app runs in the background so you can do other things on your phone at the same time ie take photo's. Regards draining your battery, I find it ok for a days walk on my phone, but as I said it is old, so ona newer phone you shouldn't have any issues.
Best way to find out is use it and try it. If you don't like Viewranger, try another, there are loads out there but Viewranger customer service is brilliant if you need to contact them. (even for non paying users)