Is an archival print washer a must???? No, but an archivally washed print is.
A couple of extra things to consider. Archival washers have fully independant slots, so putting another print in the washer won't recontaminate the ones already in there. Therefore required wash time for each print is kept to a minimum which is good because if you leave in wash for too long, the more the print is likely to curl when it dries(fibre paper).
Do fish tanks do that for you?
And for fibre paper which will require a half hour or more washing, then an archival printer is a big help for time and convenience as well being "Archival".
But for RC paper which require much shorter wash times, the wash should be complete before you've got the next one ready to go in, so a tray should be perfectly fine because you can take out the previous one before putting the next one in.
Does that make sense....