Be careful with doing this - the biggest is the extra weight/load on the adapter.
The adapters are plastic & there's risk of fatigue cracks (i used to do mounts on bicycles - it was amazing what vibrations would do over time)
I used very specific materials to really guard against this type of failure, but its still a risk you should be aware of. We're probably talking years of use before you see issues. Threaded adapters will be more prone to issues than the large variable adapters over a moderator, and springers much worse than a PCP.
The smaller & lighter the better - a single 18650 cell will last about 8hrs non-stop (what we used at exhibitions).
That is roughly a 5v 2,000mAh bank
Power requirements is 5v @ 160mA
My preference/recommendation - some elastic & secure the battery to the barrel just behind the Chrony.
If you ignore my advice & decide to put a really small one on the body of the Chrony (some have), then put all the weight as close as possible to the adapter & not the other end.
Also the weight may cause alignment issues if it sags - however the latest v5.11 software can detect this & will flag it.
Make sure you remove it & lay it flat when not in use, plastic can sag/bend over time.
I'm being pedantic here - but alignment issues are a thing with the precision of the NateChrony. 1-2mm off at the sensor can cause real issues.