Would I be declined by my new employers health insurance if I had a gap in coverage from my last job to this one?

I worked at my last company for 4yrs and left there to work at my current position at another company, and I’ve been paying cobra insurance (since I was a temp-to-hire position and am now being hired on), but now it’s down to having to pay for this month (381 a month) when I might be signed off on within the next week or two. I’m just afraid I’ll be declined if I have that gap…I was going to a psychologist for about 8mo and was taking diazapam on an as needed basis and even tried wellbutrin, and am now using klonapin on an as needed basis, these are anti-anxiety drugs…would these affect me getting picked up by the new health insurance? I just hear horror stories about pre-existing conditions declining people…