Yes, that's an excellent idea.
Propellant is mandatory for acceleration due to laws prohibiting violating the conservation of momentum.
So how to get to Alpha Centauri if you have to bring along enormous amounts of propellant? Even with an infinite energy source with a mass of only 1 gram, you need so much propellant that you can't build the ship because we only have 1 sun we can use for propellant.
Of course, if we can accelerate our propellant to ridiculous speeds, then we can use the propellant we have more efficiently. In fact, close to the speed of light, we can bring this efficiency up towards infinity, lowering the required amount of propellant down towards zero. After all, a mass at the speed of light has infinite energy and momentum (Einstein's words, not mine).
Now all we need is an energy source with low mass to energy ratio (limited by E = mc2) and off we go. Alternatively, we can grab energy from elsewhere, such as a laser feeding the energy to the ship from a home base.
Sure, that the thing is enormous, that it doesn't solve the energy source issue, and that output capacity is currently a bit too limited are all valid issues, but these issues do not detract from the fact that thrust requires propellant, that
thrust = ejected_propellant_mass * propellant_velocity,
acceleration = thrust / mass_to_accelerate and that the propellant is part of the mass we need to accelerate, thereby being limiting factor. The only thing we can do to fix it is to increase the propellant velocity. Ion drives may work as well. The point is to eject propellant at relativistic speeds. The closer to
c, the more efficient and the (exponentially) less propellant needed.
Due to Einstein's cool relativity things we can reach arbitrary ship acceleration with any fixed amount of propellant which is awesome and eliminates the need to carry several stars in the trunk for propellant.