You can run into real problems. For one thing with most of the cheap ones like your Morley you run into seriouse grounding issues. It doesnt happen all the time but alot of the time. Youll get some seriouse buzz in one or both amps. Fliping the phase reversal switch on your amp (if it has one) doesnt always do anything either. The unit needs its own phase reversal switch. Even if it doesnt do it at your house it can do it at a gig or whatever.
Plus, like Eric Johnson says, anything with batteries or an LED is going to mess with your tone in some way. His suggestion which I eventually took is to buy a Carling stomp switch and make your own. Thats the cheapest way to go. Get ahold of an old MXR box or a dead MXR effect on ebay and use that for your housing. With the carling switches when you stomp on to one amp the other one is completely out of the circuitry.
Aspect Labs makes a true bypass loop box that can function as a really good ab pedal. It uses batteries but its very transparent and Ive never had grounding issues with it. If you must go the cheap AB box route thats your best bet. Period.
Live I just use a Soldano or Bogner but in the studio I love to use multiple amps. I run 2 or more at a time and love the effect. Ive had to deal with all this stuff. Like alota things you think cheap at first but a year later and after spending tons of cash replacing things you learn whats really cheaper.