Yes. To function properly the phone needs a working battery. Usually if it's just degraded down to 80% or whatever, the battery is still very functional - you just won't get much out of it before needing to recharge.

If the battery has developed some sort of fault or has a failed cell or has super degraded or whatever, then yeah it can cause a multitude of issues, because the phone isn't designed to operate with such a battery, whatever the mode.