You can but you should let them lay flat for 24 hrs so the epoxy all sets around the insert and doesn't run down the shaft on the inside. If it runs it may give your arrow a wobble you can't get rid of.
Lots of guys hating the HIT inserts for this reason-inserts migrating when not laid flat........ operator error.
If your insert has a flange that butts against the end of the shaft...you are good to fletch when wet.
its a good idea to true the ends of carbon arrows off the saw...even with a flanged insert. The tight seated connection makes it stronger. Its a must with the HIT system.
Agreed... also the less the epoxy gets disturbed the more stable it cures. You let any epoxy build up at the end of that insert or just on one side of the arrow the epoxy builds a little bit you get an arrow the always spins and lands with that epoxy build up on the bottom. Bugs the crap out of me. IMHO you arrow should spin from any position and stop at different points every time. Same concept of balancing a car tire I spose
Another bit of advice on the HITs...I found that the suction generated by pulling out the green tool can also pull the insert out a little. The fix is to use sandpaper and take off a little of the two rings on the tips of the tool, just enough so the fit is not tight. Then I check the depth of each insert by laying them side by side, perfectly aligned, and looking in them with a light. If one gets sucked out a little I can then use the tool to reposition it. If one is too deep (which is rare) I then use a Gold Tip FACT rod to push it out from the nock end so I can readjust it. Finally, always pull the nock before installing insets because the air pressure can also push the inserts out a little before the epoxy cures.