Hey there Samish!
If you've got no bars, but you've still got 4G, that generally means your phone's clinging onto 4G for dear life. Depending on your carrier or how strong your signal is in ASU, you might still get some notifications, you might not, If your phone's on no bars, and you want notifications, try bumping your phone down to 3G and see if that pulls anything through.
Hope this helps,
Tom 🙂
ASU - Arbitrary Signal Units - Find this reading in Settings > About Phone > Device Information > SIM Card Status > Signal Strength