For the OP ....
It is entirely up to you. Personally I would do it... my previous results make me biased.
FWIW... Loctite sells "LOCTITE 620 is a high strength, high temperature resistant retaining compound." Good up to 200 degrees Celcius.
I believe 609 is recommended since you could heat the upper and more easily remove the barrel if needed.
I have used 609 on numerous uppers and barrels... many hundreds and hundreds of rounds later , no issues.
NOTE... my test involved lapping the upper receiver face "true" , making sure of a snug fitting upper to lower, smooth gas tube interface to the gas key, and using the 609 Loctite.
And my results were improved precision... not with every single brand ammo, but more then enough to make a believer out of me.
Some of the improvements were flat out dramatically better.... much smaller groups, and certainly more consistent groupings.
I swear there were less flyers.... but my less then scientific recording and average Joe testing certainly couldn't stand up to a court of law, Lol
Criterion Barrels has a video series on the "
Criterion Barrels Releases “Accurizing AR-15” Video Series
Part 3 , at the 50 second mark, shows them using the Loctite 609.
https://criterionbarrels.com/media/accurizing-the-ar-15-video-series/?v=00dc5da36527
All that said, SS shims and thermal fitting can produce snug fitting barrels.
I also strongly suggest lapping the upper receiver face... the video shows what I mean.
Ultimately... do as you see fit with your rifle.
For those interested... ( pardon the poor writing skills and presentation... I am not a writer... I am a mechanical guy, and work with my hands. )
PSA OEM 20" Barrel before and after the Assm. tricks
https://www.ar15.com/forums/industr...-gas-upper-review--PSA-Nailed-it-/301-285762/
My best group to date from my 6.5CM 22" Criterion barreled PSA upper and lower. Shows the barrel can out shoot me. ( The flyer is my fault 100% ) 10rds Hornady 140gr AG , 100yds , scoped, benched .. etc.
Assm. tricks listed above used.
Yes, Cherry picked... I am proud of the group.
FN 308 CHF CL Barreled, PSA upper and lower , same assm. tricks. ( second photo ) 10rds 155gr Hornady AG, same bench shooting