Yes, aliases can read/write to the same DB/table. I do it. I have 4 domain names that are all aliases, and no matter what domain name is in the URL, it can access the DB... b/c it's the same 'localhost'.
As well., after they're logged in, generate a random #, and add it to a column in the table like a unique id #. Then just pass that number from dom. A to B. Dom B. then checks to see if that random # exists in the auth table, if it does, pull that user name/data you need.
As well, for cleanup, set a timestamp in another column in the record, then create a page for a cron job that runs every min/hour/day/week/whatever to delete any auth records older than xxx # of mins/hours/days/etc.. Or just have the table clean itself up everytime it's accessed. So while it does a check to see if that # exists, have it delete any records older than xxx mins/hours/days.... etc.