It is possible you can't get CHICK Quinn (I only started Quinn paths from Season 3 on these recent playthroughs and set the affinity when starting, and haven't gone back through to check), but you can definitely get DIK Jill. It's difficult, but not impossible.
Both options (Chick Quinn / DIK Jill) are impossible in a normal gameplay without using a console, URM, or cheats. Strict checks here and there and special conditions simply don't allow this to happen.
Your romance with Jill is over in EP7 if you have a DIK aff during the choice "fight for her" or not. Despite you choice it's the end of relationship if you are in DIK zone. Even if you'll manage to pass this check being Neutral, you will never get a DIK aff after, bc you did too much of Chick choices previosly.
Maximum you can get with Jill is a Neutral aff. This way you can do drugs to get an additional content with her, bc it's seems to be a sensitive topic to her (Lana).
Same goes to Quinn, but here it's about the DIK choices in summary, the ones you had to do to stay on her path and the affinity check in EP6. You can't be Neutral or Chick at EP6, and to get the DIK affinity up to EP6 you have to make more of DIK choices than lets you stay at a Chick zone in the end of EP8.
Maximum you can get with Quinn is a Neutrall aff. Here are not a lot of visible changes. Probably nothing, if I remember correclty.