"If you assume that they can accelerate past the speed of light, and that there are no diminishing returns, maybe.

Keep in mind that the faster they go, the more fuel it will take to overcome the inertia of acceleration the interstellar hydrogen to the speed of the ship.

Also it should be obvious that they will spend much of the trip acceleration and decelerating. If they traveled at the speed of light the trip would take 100 years. Certainly given all the constraints, their trip would take considerably more than 100 years. "


Nope. look at it relativistically:

one accelerates at a constant 1g, until the halfway point, then one flips the motor and deaccelerates to a stop at the destination.

Time dilation ON the Ramjet means that it would only be 20 years to the pilot, going a distance of 60,000- 80,000 LY. Since time is dilated the ( near- lightspeed) portion will cover most of the distance in almost no ellapsed time. (As long as one does NOT slow down to look at things along the way) A longer journey would be even more effective- one could cross half the entire Universe ( about 13 billion LY) in a single human lifetime (70 years). Make it a generation ship, and a few generations could go to the collapse ( if that happens) in a few hundred billion years- but time dilated to a few hunderd years ellapsed on-board)