I've thought of this, but this particular Timmy's is right around the corner from my house and honestly cuts time out of my morning commute. Would rather keep my mouth shut than give up a good reliable thing I got going.
The relationship probably wouldn't work out anyway.
She's the girl of your dreams and you're going into it saying it probably won't work out? You make that thing work out.
She clearly knows who you are. Just step it up next time. Ask her when her shift ends. Ask if she wants to go for a coffee...then laugh about it because she probably hates coffee after serving it all day.
But seriously, just ask her out. Say, "hey, what are you doing after your shift?" and then go from there. You're in the drive through, so you hve the benefit of keeping it brief.
"Hey, what are you doing after your shift?"
depending on her answer you can then say, "When do you get off work?" Then she can answer with the time and you say, "Cool, see you then." and then drive away. No time for it to get awkward
AND THEN BE THERE WHEN SHE GETS OFF WORK! If you're at work when she ends her shift, tell your boss you have the runs and need to go home. Don't nobody mess with the runs. That's a get out of work free card. Just use it wisely.
Don't live in regret, man.
What's the worst that can happen? Even if you get shot down, go back for coffee the next day and act like everything is normal. she'll either appreciate the effort you're putting in to pursue her, or, you'll just get over the slight embarrassment and you can keep getting coffee at your local Tim's.
It's a small risk for a potential huge reward. Go for it.