Yes and no.
In singleplayer, the AI never builds any real new capital ships (and making capital ships after 1940 is a dubious prospect if you aren't planning on a very long war; the construction time is too long). As a result, the 1936 tech is good enough for most new capital ships (battleships are too slow in my opinion without 1940 tech or a designer speed boost like those of France and Greece), and the Super-Heavy battleship is far more powerful than newer battleships (they do, however, provide very good engines).
1.) Hulls: SHBB is a good tech for fighting large fleets, as it is the best straight-up battleship hull for fighting other battleships. It isn't strictly necessary, however. Later BB hulls are good, and in particular offer new engine upgrades (which are essential to getting decent speeds), but the delay in building them isn't really justifiable. Cruiser hulls are more realistic as you need light attack more than heavy attack, and you can build cruisers in wartime.
2.) Guns: Light and heavy gun upgrades are AWFUL. The only gun upgrades that are worth anything are secondaries (DP secondaries are awesome), and cruiser guns (they also add significant firepower and piercing, but at the expense of costing steel per turret...). Never research past 1936 light or heavy guns.
3.) Radar/AA: These are the good refits. AA gets vastly-better in 1940 and 1944, and RADAR massively-improves capital ship attack ratings starting in 1940 (the first two radar techs don't really add any attack). Fire control is a toss-up since it lowers reliability.
Past 1940, its rarely worth making new battleships. If you can use a research bonus to get the 1940 hull tech, its useful for making faster engines available for new ships, or stick to battlecruisers (which have decent speed, at least). Heavy cruisers are pretty good after 1940, but in singleplayer you're not likely to really need that many new capital ships into the late game.
Refits are worthwhile on capital ships, just don't refit engines if you're not trying to upgrade ships to treaty standards (i.e. the USA can't really get any new capital ships without getting rid of some until the war starts). Never refit armor either, and I'd only refit guns on CAs if you want to downgrade them (otherwise its expensive to upgrade them, but some nations like the USA have way too many CAs and not enough CLs). AA, radar, DP secondaries, and maybe fire control (I don't like the loss of reliability, but it does significantly-improve attack and AA) are all worth refitting. Refits are also great since they don't cost any steel, in case you're running out (unless you're adding a component with steel requirements).
