Can I ask a girl if she would go out with me if she was single (has a boyfriend)?

ThatOneUnluckyGuy
Short version: she has complained to me a lot about her boyfriend and then they broke up. Now they are back together but "not fully back together". I think and care about her way too much to be friends for nothing

Long version: we're co workers and have been constantly flirting and making sexual jokes with each other. I've known she had a boyfriend and had backed off as much as I could but then she went through a huuuuuuge argument with her boyfriend. Less than a week later I asked if she was going to a camping trip with a few other coworkers. My plan was to ask her out then but she said she couldn't because she didn't have enough money to pay for gas. (She was off work for 2 weeks in the hospital and recovering from broken bones in her hand. Her own fault from the argument, not caused by boyfriend.) So I gave her $50 and she started crying and saying how that was so nice (I found that to be odd). She said she could probably go after she talks to her ex (still her roommate). She never showed up and later when I asked what her relationship is with him she said they are "dating but not fully back together" (I don't know what that even means). I jokingly said she should dump him and she said something along the line of he still could change and she is giving him till the end of summer. I told her I'm interested and to talk to me when she was single. A few days later I asked if she wanted to go to the dog park and we both brought our dogs, talked for like 2 hours and smoked a joint. NOW I want to hang out with her but I know it's only going to make me fall more for her so it's it too much to ask if she would date me if she wasn't already dating?
Can I ask a girl if she would go out with me if she was single (has a boyfriend)?
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