I'm going to agree with Sapphire Chan and Butterfly Mommy... In general, TV should be a big no-no, but I think there are exceptions that CAN be made, with MOST children, when carefully monitored (ie, watching for the 'hypnosis')
We didn't use Signing Time, but another signing video, "My Baby Can Talk." We LOVED them. We did signing in context around the house, and we even took a class. But it was the videos that clinched it for her. She learned so much from them.
I do prefer MBCT over BST in part because it is slower and less glitzy, less 'addictive' in its presentation. It's very simple... classical music background, toys and animals and children demonstrating what the meaning of the word is, and an adult and a child demonstrating the sign.
There were times when DD would watch it over, and over, and over again. For days on end. And other times when she would ask to watch it, turn it on, watch 2 minutes, then run off to play with something else. And times where she showed no interest in it for weeks on end. It's like any kind of learning with toddlers -- they will 'cycle' through things as they go through developmental and learning phases, obsessing over something for a period of time, then just... moving on.
Pretty much the same thing happened when we started letting her watch movies, around age 2. (We don't have cable, so no 'regular' TV). She would completely obsess over a particular movie for about a week. Demand to watch it all the time. Memorized all the lines. Play-acted that she was different characters. We'd be starting to think, "gee, maybe we've been too lenient with this and this isn't good for her, we should cut back." Then she'd stop. Move on to something else.
So... so far, we're content that she is able to self-regulate appropriately with TV movies. She ADORES them when they're on, but doesn't freak out when they're not. She did move through a phase where she DID freak out... but passed through that. At least right now, it all seems good. I think part of it is that she does have enough other creative and interesting activities -- I don't mean fancy toys. But opportunities for imaginative play, with playsilks and art and blocks and lego... so she's not just constantly being drawn to TV out of boredom. That may be a factor for some kids.
And some kids just aren't able to self-regulate TV, period. My son is one of those. We tried letting him... tried waiting it out, until he moved through the obsessive phase... it never happened. His personality (ADHD and SPD and lots of fun stuff) does not have the executive function control or self-motivation to mediate his activities.
So, it can totally depend on the kid. All you can do is -- if you're comfortable with it, try it, and see what happens. Odds are they'll be fine... but if not, then you will have the monster to deal with when you REMOVE the TV privileges. You know your kids best, you may have an idea already whether you think your child will be able to handle it or not.
You also didn't mention how old your LO is... if they're under 2, you definitely need to be more careful. I personally still think that signing videos are acceptable exceptions to the nothing-under-2 rule, but I know not everyone will agree with that. But under 2, most don't yet have the self-control etc to self-regulate TV watching and are more prone to the addictive influences. I wouldn't do a free-range approach with videos under age 2, but I don't see a harm in parent-regulated watching (especially if the parent is watching WITH the child as well).
Not everyone will agree with that and I totally understand where they're coming from. I wrestled with it myself. This is just where I ended up landing.
Hulu.
I actually like watching the show's 
and watch them with DS.
