Not necessarily, Proxima is about 4.24 ly (268 AU) from the sun. New Horizons took 10 years to reach Pluto (39 AU), so it would take 70 years to reach Proxima given it's speed.
Now, let's say that we would use the sun for a good slingshot, it would take less then a year for that, but afterwards we would aquire enough speed (probably at least more then twice that of New Horizons).
To reach (almost) lightspeed, one would require a lot of fuel, and to slow down, the double. And ion-like engines have a too slow acceleration/deceleration, which too must burn constantly.
Anyway, to get into orbit alone, rockets would suffice, but to go out there, something else would be required. Otherwise we would have to send drones and probes to be our eyes.
As far as physics go, it is not possible to go beyond lightspeed using conventional acceleration, due to inter-atom bonds becoming weaker due to their relative speed and also the friction with radiation pressure outside of the solar system. I also suspect that the void isn't really a void but some kind of super liquid, which is influenced by gravity, just like a vortex in water. And if it's true, then this also would have to be taken into account.