Will a cell phone battery drain faster if it is connected to multiple bluetooth devices simultaneously?

Probably as it is sending and receiving info from multiple sources.

Logic would say so.

Surprisingly, no. Basically, bluetooth is either on or off; there is no middle ground, no varying power levels, or anything like that.

One thing that will drain your battery is being someplace with poor reception. When I lived in NH and had poor reception just about everywhere (usually 1 bar, rarely 2, never 3+), my phones would die in a day or less. The same phones in Seattle (4 bars everywhere I went) last 2–3 days between charges; the better reception allowed them to turn down the power on their transmitter.

But like I said, Bluetooth operates differently.