I do believe the debate of RAW vs. JPEG as been beaten to death. Most people agree on this - Shoot RAW if you if speed and size are not a variable, however shoot JPEG if you need the extra write speed and size difference. Also, JPEG gives an advantage of on-site printing for things like photobooths (the white balance, sharpness, etc. are already set ahead of time, and there are no changing variables that will need to be edited later).
Right now what you are doing with your camera is actually somewhat silly, if you have the space you should be shooting RAW. The process your camera is going through to shrink that image actually causes a greater loss of image quality than you may realize. It is like shooting yourself in the foot before a race. Sure you can still run, but it is going to show that you aren't at your best.
Now that those two things are out of the way, we have the question at hand - "If I use medium JPEG quality for the most part, will using high quality lenses like Canon L series really matter or would I have be to shooting in Raw with medium to high resolution?"
Any time you improve equipment, you will see an improvement regardless. This is why people become obsessed with buying new gear all the time. Regardless of the settings on your camera, as long as the only thing changing is the lens - you will see an improvement. There really isn't a question involved here, just an insecurity about whether or not you should buy something new. If you can afford the lens without putting yourself in financial trouble, and you know that photography is a passion that you will not drop, than go ahead and buy the lens. I would suggest that if you do invest in such an expensive and professional lens, that you start understanding photography professionally and on a larger level as well. This is a serious investment, and it would be wasted if you didn't learn more about how the camera works. You don't need to understand everything, however based on the fact that you don't know the answer to this question I would probably say you aren't really ready to appreciate such a lens. Consider learning about how your camera works, and the process involved in editing digital negatives.
Now that I've been a bit mean and serious I will say this - If you can afford it now, and pay for it, I see no reason to deny yourself such a great piece of equipment. You can always sell it down the road. Just learn more about photography and DSLRs in general, or that investment won't see a ROI. Your best investment, would be to buy terrible equipment first. Learn why a lens can be bad, and how a bad lens can be used well. Then move onto something more serious like L series glass. I have abused the nifty 50 - 50mm 1.8 from Canon so much that it actually broke in 2 years use. It was a cheap lens, and it taught me very well that working within limiting boundaries still allows very much creativity. It will force you to think outside of the box more often than not.
I don't know how serious you are about photography, but assuming the investments you have made (and are willing to make) it is clear you enjoy it a lot. This is the only reason I've posted this as if you want to be a professional on some level. If all you want is photography as a hobby, you can pretty much ignore whatever you want.