As far as I know, Yes, all the gaskets, bearings, freeze / pipe plugs, and rings are the same.
Significant Differences between 343 and 360:
Deck Height - 343 = 9.175 ... 360 = 9.208
Stroke - 343 = 3.28 ... 360 = 3.44
Pistons - 343 4V had flat top with valve reliefs. 2V had small dish
......... - 360 had a "large" 28cc dished piston '72 & up
Exh Port - 343 = rectangular ... 360 = dogleg
Chamber - 343 = 50.60cc ... 360 = 57.92cc late '71 & up
Crank Flange - 343 = BW flange ... 360 = TF Flange '72 & up
Dampener - 343 = 3 bolt ... 360 = 4 bolt '73 & up
Flexplates were different for C.I. and Trans Type
As mentioned, the 343 rebuild parts should all work with the
360 dampenr, flexplate, crank, block, rods, heads, etc.
but re-balance the rotating assembly.
May I ask, are you considering a 343 Kit from www.egge.com ?
If so the pistons may have a ~.030 shorter compression height than stock.
Info Egge provided to me was 1.570 Compression Height for their 343 pistons, both 4V & 2V.
Stock 343 & 360 Comp Ht is 1.601 nominal calculated from info in PAS.
Be sure and consider that when calculating CR and deck clearance.
Some of that can be "re-gained" by offset grinding the 360 crank, and/or deck milling the 360 block.
If Con Rods are re-conditioned they will get a few thousands shorter.
Using nominal values,
3.44/2 - 1.72 throw + 5.875 Rod + 1.57 CompHt = 9.165
360 block Deck Height = 9.208 - 9.165 = 0.043 Deck Clearance.
Understanding is the egge 343 4V piston has 3cc valve relief volume
and the 343 2V piston has 14cc relief / dish volume.