Does turning off cellular data significantly improve battery life? I almost always turn off cellular data when I lock the screen. I only turn it on when I’m using internet. But it’s annoying to do that almost every time. Does it worth the trouble?
You can follow general rules to optimize your battery life.

https://www.apple.com/batteries/maximizing-performance/.

Now respecting your question, you save a lot of battery by turning cellular data only when you needed. Cellular data consumes a lot of battery power, specially when yo have have no coverage or low signal:

"No Cell Coverage and Low Signal. This indicates that either you are in a poor cell coverage area and your iOS device is searching for a better signal or that you’ve used your device in low-signal conditions, which has affected your battery life."
This is according to previous apple link, however, take into consideration that GPS works with cellular data so if you leave it by accident powered on, your battery charge will decrease dramatically.

Also I recommend you to have your iPhone up to date, for possible bugs, of course back-up first.

https://support.apple.com/en-us/HT203977

Pay attention on one detail, if you back-up an iPhone with already performance issues, the iOS or iCloud back-ups could be affected too. So it is important to back-up often and not wait to have problems to back-up before an up date or even a restore.

Kind regards!