Sleep Talk isn't all that unreliable, particularly for Zapdos. All 'mons in GSC care about either Thunder(bolt) or HP Ice. That gives a 2/3 chance of Zapdos doing something relevant (Resting or attacking productively) per turn.But Blissey isn't supposed to stay in against the electric legendaries all the time. If she forces them to use Rest and then you switch to another pokemon who can take advantage of a sleeping Raikou/Zapdos, she has done her job. While they're sleeping it's them who create free turns for you, given how unreliable Sleep Talk is.
And, yes, this is an effective strategy in GSC.
And the thing is that they don't have to stay in. They can, but they don't have to. Your opponent can switch in whatever the hell they want while Blissey sits there blobbing.
Let's set up a comparison table, just for the lulz.
If they stay in:
vs Snorlax they die
vs Raikou Zapdos dies, Raikou's potentially bait for Spikes/Roar shuffling
vs Blissey they sit there and have to Rest occasionally, can shuffle in Raikou's case
If they switch:
vs Snorlax they've typically got one or two possible switch-ins (depending on set); a lot of offensive teams are taking relevant damage anyway (+1 EQ on Steelix etc)
vs Raikou they eat Thunder unless they've got a Ground; even then it's mindgames
vs Blissey they can switch in 2-4 things: there's the obvious Snorlax but you can get Rest turns off Suicune/Tyranitar/Umbreon/whatever, go for a TrapPass (or anythingPass, really), attack it with Gengar (Hypnosis scares it out, or there's DPunch), spin with Starmie, and then you've got the set-dependent stuff like Forretress for Spikes/Spin or Steelix for Cursing/shuffling if it doesn't Flamethrower, Nidoking if it doesn't Ice Beam, Vaporeon if it doesn't Light Screen (and heck, even if it does), Miltank for a Bell if it doesn't Sing, Machamp/Missy if it doesn't Toxic, etc.