For starters, every time you astart or accelerate, you're accelerating close to an additional 2lbs. You are going to feel that, and it will add up over 120 miles.
Next, the rolling resistance will make a difference in time. Assume the rolling resistance makes a speed difference from 13mph to 13.5 mph, (and I think that's a conservative assumption, the Kruezotter calculator puts the difference at almost 1mph) the time difference is 20 minutes.
Then, climbing over 30 miles around 5% grade, the 2lb weight penality is going to cost you 5 minutes or so.
All considered, I think it's very reasonable to assume that the OP would be at least 15 minutes, and maybe 30 or more minutes slower over 120 miles on wide touring tires, than he would be on racing tires.
If you're at the edge of making the time cutoff, that 15 minutes could be critical.
Thus, if I were the OP, I'd both train, and make smart equipment choices.