EMT-B to EMT-P to RN ADN to BSN here and I still think of myself as a paramedic, it will always be my first love.
To answer the OP's question, did my medic training help my nursing career? Absolutely but I was a medic for some years before I was a nurse, meaning I had a lot of experience before I ever went to the Paramedic to RN bridge program. Got to say, my critical thinking and assessment skills were learned as a medic and were a cut above what was taught in nursing school.
I would not recommend anyone get their paramedic's license with the idea of immediately going into nursing school while learning a new trade. It's far too much to be a new medic while trying to assimilate nursing school as the same time.
How do I know?
I flunked out of my nursing school by working a shift where I go no sleep then taking an important exam which I bombed. And, I wasn't new to the field. Sat out a semester and went back into the program. Lesson learned, I quit my job as a medic and completed nursing school, it was easier eating ramen noodles for a year than taking a chance on failing again.
All the above having been said, the reason I went to get my RN is simply that my body and pocketbook wouldn't handle the strain any longer.
Too many years on the road, walking backwards down a flight of stairs at 0200AM carrying my share of 300lbs of humanity for (at the time) $12.00/hour. I have one artificial knee, the other bone on bone and a bad back.
Still miss the road but looking at my back account, maybe not as much as I thought.