Yes, it has a huge effect, I find. My lv 120 character is virtually unplayable, so more often than not I just find myself creating new ones to be able to play.
There are ways to make it better, though, I just can't be bothered most of the time. You can download the Unofficial Patch (you should really do this anyway), apparently waiting a month or so (only in-game, don't worry) resets cells and containers and that should help too.
Also, if your game regularly crashes as well, it might be worth cleaning up your modlist with tes5edit or something, that should help a lot.
It is my my understanding, however, that the bloat (and thus the sluggishness) never fully goes away, as the further you progress, there's inevitably more stuff for the game to remember.
The easiest (and least time-consuming) tip is to disable autosave, this helped me a lot. (But don't forget to periodically save manually, you know.)
Otherwise, you could just pretend your character is getting older, or the weight of the tough decisions they've had to make is slowly eating away at their will and makes them more reluctant to go forward. Remember, the difference between a bug and a feature is just your attitude; this is a Bethesda game, after all.
