Is it bad practice to look for a job while you have a signed offer?

So I’ve been at my current job for about three years now. I’ve never been crazy about it, but it was an alright first job straight out of undergrad. I was able to switch to part-time when I started grad school last year and have been planning on staying with this company until I graduate next spring. Management’s never been the best at being responsive (making me feel very unappreciated), but lately they’ve flat out ignored a time-off request, which has me expecting the worst. I’ve already signed an offer for a job I’m really excited for that starts next summer, but have been wondering if I should just leave my current company and work another part-time job until next summer. Is it bad practice to go into a job knowing I’ll only be there for a few months? Would my future employer care at all if they found out? I’m thinking about going through Robert Half and explaining my situation to them.

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