It would take 230 years, to be relatively exact, at Reaper FTL speeds and over 500 years at the stated FTL speeds of the council races.
But the time isn't the issue. Drive discharge is. They would fry long before they reached Andromeda, unless they somehow found a way to reverse engineer reaper tech and negate drive discharge.
Its electric charge, right? I assume the mass effect spaceships are made of some ceramics or plastics (composites) if the charge is a problem for anyone inside the ship. So the solution would be to build the ships with iron or other conductive material so the charge will be only on the outside surface according to physics.
Other solution would be charging with negative potential compared to the drive charge. What is a good way to accumulate static charge? Cats. So you fill the ship with cats and give them some device where they can each in turn go and neutralize some of the drive charge. Problem is ofcourse that you need plenty of catfood and sandboxes for them. Maybe even mice or rats for them to hunt during the long flight.