TLDR: Cheap optics - the image gets worse with each new element added, pretty quickly. High end optics - the image may get better, may stay pretty much the same, or may get worse; if it does get worse, it's by such a small amount that you can usually ignore it. This assumes a scope that is in good shape, otherwise all bets are off.
Now the long version:
A T-adapter normally has no optical components, so there's zero loss of quality there.
Anyway, some actual answers: It's all a matter of price. Use cheap mass-produced optics, and the quality will degrade pretty quickly. Use more expensive elements and the image will stay amazingly clean even after passing through a large number of optical elements.
A cheap Plossl eyepiece has only a few lenses and the image looks like junk. A Tele Vue Ethos eyepiece has 9 different lenses in 5 groups and the image looks incredibly sharp.
Keep in mind the quality of the primary mirror is also important. Many mass-produced scopes come with primary mirrors that barely pass the Rayleigh criterion. Some are randomly better. The secondary mirror also matters. The corrector plate again introduces its own problems in catadioptric designs.
"Amateur" doesn't mean much. A mass-produced GSO-made dob is "amateur". But so is a clone made with optics figured by a reputable optician. Yet one might be a terrible less than λ/4 instrument, end to end, while the other may well be above λ/15 and pretty high Strehl factor. Looking at tight double stars, the loose instrument may not even resolve the pair, while the good optics may put a clean sharp sliver of black between the two Airy disks. One will show a few stripes on Jupiter and not much else. The other will show plenty of detail. Their performances will be very different. But so will be their prices.
Each element in the optical chain matters, and their individual performance levels are very much dependent on price. A single cheap element may ruin the image, while you could add tons of high quality optics and the image stays sharp and contrasty. This is all with amateur components that you will actually see used by various folks when your local astro club throws a star party over the hill south of the city.
And then there's collimation. There are folks out there who ask "what is collimation?" :) for cryin' out loud, people, that is not acceptable. The best optics in the world will mean nothing if the scope is not well collimated. The best car in the world will not work well if you forget to change the oil.
Then there's seeing. You take your expensive hand-figured scope outside, and seeing is terrible. You may as well look through a pirate's spyglass, that's how bad the turbulence is. And then the next day the jet stream moves over some other place, and you get clean, pristine, sharp views.
Then there's thermal stabilization. A cheap mass-produced dob with a fan blowing over the primary mirror may actually beat the custom-made clone with no fan. Well, after a few hours the fanless clone may catch up thermally and its view may improve a lot (or not), but you get my point.
Goes on and on. There are no simple answers.
EDIT: Sometimes the image is improved when you add more glass. This is obvious in fast newtonians (F/5 or faster), where coma is visible in the eyepiece. But then add a coma corrector, like a Paracorr, to the optical chain, and the image is dramatically better. In fast newts, only with a coma corrector will the high end eyepieces achieve their whole potential. Low end eyepieces need not apply, their own problems are worse than coma.
Same idea for astrographs: the field of virtually every scope is curved. The sensor of virtually any camera out there is flat. That's a mismatch. Add a field corrector and the mismatch disappears. The image gets better when you add glass.
Heck, if you're ambitious and design a short achromat refractor, you will get chroma trouble in the eyepiece. But then filter out the offending wavelengths, and voila, no more chromatic aberration. A lowly filter has improved the image. Sure, the image is tinted, but the overall resolution is better. (this is a reason why you don't see short achromats too often)
Let me confuse you a little. All of the above was a "whole field" discussion. If we're talking about strictly on-axis performance (for folks who do planetary observations in tracking scopes), then less glass tends to be better. Again, if the glass is low quality then it's no good, but as a rule, if you watch a very small low contrast target like a planet, and keep it on axis, then there are eyepieces dedicated for this kind of thing that manage to eek out a tiny bit more performance from the scope by using clever minimalist designs.
Some people have even tried ball lenses, extracted from laser couplers, which are just simple balls of glass or sapphire, and reported a very small improvement for on-axis planetary observations, compared to any eyepiece. These are not mere glass marbles, but high quality optics; a tiny 9mm ball like that might go for \$20 ... \$40 online.
But this is kind of a fringe issue (unless you have a very special thing for observing planets, in which case you'll see this discussion in a very different light, so to speak).
The question you asked is very complex.