You are guaranteed a trek through the tunnel. *IF* you get to the gate on time, and it's near a tram or close enough to the tunnel, you should be fine. If you're stuck in the gates between trams or you're late, you can expect to run. That being said, you're probably getting on a crj so you don't have to worry about overhead space as you'll be planeside checking, and preboarding may not be a concern.
If it was me, I would do it but I like to tempt fate. Check and see when the next flight out is if you miss it and calculate your risk.