Yep, those checks are all worth doing.
Don't use the impulse starter to check spark with those cowling bolts missing - all too easy to break the engine cup.
Unless the engine has been full of water, there will still be oil in the bearings. The bore is more prone to rust, from damp air, than the bearings.
It might be cheaper to find another 3 series carby with the tickler, and do a swap of bits. It's quite possible for those ticklers to just fall off, if the brass retaining wire breaks due to age and wear.
A seller called 'mowtimepast' on Fleabay currently has a couple of NOS P/No 3-136 'Tickler repair kits' [tho' he calls them a 'victa 18 or rotomo primer'] on sale, but $29 inc post is maybe a little steep...
