Would a bad battery cause signal loss?

So for the past 2 weeks, my phone randomly would go in and out of service (4g & phone completely to 🚫) then if I play clash of clans or on an app too long, it shuts down. When I start it back up immediately it's at 2%, always. If I shut it down, then turn it back on, it's at 60-75%. Never encountered this before with signal loss randomly but phone shutting down yes, just wondering if anyone experienced or have heard this can occur. FYI I had MochaDrizzle ROM running (fast as hell), then went to R3ds, and now back to stock, all still occurring, even flashed the 4.4.2 baseband modem or whatever also. Thanks guys!