They can certainly handwave-away the time travel issue with something like this, yes, but in the universe of the Potter story, time travel is heavily monitored and regulated, and Time-Turners in particular were confiscated and out-of-commission by 1997 (when the Ministry ride may be set).
Also, I'm not 100% sure, but I believe in the lore of the Wizarding World, time travel only works for going into the past (and returning). So if we're starting out in the 1920s, we should only be able to go further back. I think.