Cycling a Tank

Yes and no. Once the tank has started cycling, it goes until it's done. If the fish are going to be taken out anyways, it's better to just use some store bought jumbo shrimp to get things going (better to do this anyways). However, you said a couple of months. Cycling generally only takes a month, sometimes as little as 2 weeks, and sometimes as long as 6 weeks. A false cycle can occur when bacterial populations never truly build up to what they need to be to get rid of ammonia, but I wouldn't worry about that. So in short: yes, it'll continue and it'll only take a month

feeding bacteria

You can also keep the bacteria alive by either feeding a bit of fish food to the empty tank, or by adding a bit of ammonia to the empty tank.

Or you could move the filters to the same tank with fish and when you need to get the other tank going, just move one filter over.

I have cannisters on the two larger tanks, but one holds a spare HOB filter that is running. should I ever need to sert up a Q tank (now dry) I can take that running HOB filter to the Q tank, and start up a spare HOB in it's place. (I got lots of small HOB whispers at garage sales last summer)

I figure the tank with the cannister won't really miss the HOB much, and the Q tank will be so lightly stocked with fresh water that the load won't be much.