I understand that unless I get a tune I will get a CEL, but is it safe to run a catless DP without a tune for a few months? I want to get a front mount and a few other things before I get tuned, or should I hold off on the parts until I am ready to get a tune and do everything at once?

The car will run fine with a catless DP, you just get a check engine light with a 420 fault so be ready for it. You'll actually feel the power gain from the DP even without the tune.

I have run catless for 25k miles with no tune and no problem. I do recommend that you buy a new gasket that sits inside.
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You can run a Mini without a tune, but you will always have a Check Engine light on. You will know if your car is throwing one of the countless other codes the CEL represents. Also, you most likely will fail your state emission test

mQubed Motorsport, Manic Tuning Dealer