Depends completely on the types of games you play. Your best bet on finding out about any game you play and how much HDD access it does in game is to probably google for forums/optimization guides for that game.
In some cases an SSD will improve load times but make no difference actually in the game itself - I suppose load times from one level to the next could be considered as 'in-game' but generally isn't seen as such.
Certain games follow typical patterns, although in some cases may vary depending on what allowances the game has to make for the amount of system or graphics RAM available, etc.:
E.g. Source based games (Counter-strike, Half-life, Left 4 Dead), and other FPS games (Unreal Tournament, Quake, Doom) typically pre-load a large amount of the game level data in to memory and access the HDD in-level for things which are triggered by events in the game (e.g. sounds like explosions, speech, etc.).
In most cases the penalty you pay in terms of in-game performance isn't too bad as these are not massive files, but you may still notice a small drop in performance when this happens.
A lot of simulation games like racing games work in a similar method but probably do even less access whilst in-game.
Free-roaming / open-world / MMORPG games (think World of Warcraft / Guild Wars 2 / maybe GTA4??) work in a similar method however do a lot more HDD access in-game loading graphical/3D data also as you move around. Depending on the speed of your system the hit can be relatively bad and drop your FPS down whilst data loads - also you may have the side-effect of seeing things suddenly appear as you get closer to an area (as opposed to coming in to view with and like the land as you approach) and then also noticing textures automatically over a few seconds improving as the data loads.
In this sort of situation an SSD may help provided your system itself isn't a bottle-neck for the data, but that said, any relatively new decent HDD should be adequate in such games - I'd have thought the 1TB (provided its not some green/eco version) should offer decent performance.
As for the drive cabling, there is no 4-pin connector on modern SATA drives - during the transitional phase to SATA some had the old 4-pin molex connector also, however I'd expect your drive to have just SATA power and data connectors.
E.g.
©Toms Hardware
If your PSU doesn't have a SATA power connector you can get adapters which plug in to the molex connector and provide a SATA power plug.