It is a very good question, actually. And yet, how you formed your question the answer is very clear: can poor image quality have a negative effect on user experience? -> absolutely, it can!
Sure, so the question is: what to do about it? What are good ways to have a good website performance as well as good image quality?
you can and should use higher quality graphics for retina displays in my opinion, and know that those graphics (if you implement them the right way) will only be used for devices with retina display. Devices with "normal" displays will continue to use the other graphics. So, you need to provide two resolutions for each image.
yes it is true that devices with retina display will not always have a fast internet connection, as it is true for devices without retina display. But, first this will change in future as there will be many more services and features available so it is just a question of time. If you look into the future, do not worry about it too much.
Secondly, for users with slow internet connections your site will not be the only one that takes a lot of time to load. This should not be an excuse, but what I mean is that it is similar with users using old web browsers - they are in the minority and do not expect your site to be different from any other.
And finally, yes till now only the iPhone and iPad had retina displays, however now the first MacBook Pro with retina display has been launched by Apple and you can expect that somewhen in the future also the laptop lines and desktop computers will have higher resolutions.
What are best practices and solutions?
use as little images as possible! For anything related to the layout, do not use images at all if you can. This is easier than ever with CSS3. Example: I've heard (never checked actually) that the menu at the top on www.apple.com is only CSS-based. So, a lot is possible nowadays.
know how to compress images in the right way! Read about the difference between JPEG, JPEG 2000, GIF and PNG. Good image editing programs can compress images very well without reducing the quality a lot. Very easy - think about sites like facebook or flickr, they have to deal with millions of photos and many photos on one page - so it IS possible.
to perfection user experience: you can preload images. Google does this without you knowing, if you e.g. enter a search term it already starts preloading images of the first listed results.
and nevertheless: think of which photos are really necessary to be displayed as well as the resolution. Also, when loading the site, does loading images stop from loading the layout? Try to first load the layout and then the images.
Altogether there are often many other things you could improve before it comes to reducing image size. Often people focus on reducing image size on webpages without knowing that actually third-party plugins like facebook's social plugins slow down the site much much more than any image would do.