Sounds like progress. And you've learnt something about dogs...
The lack of bush preload on its own wouldn't, but if the rear control arm pin isn't seated properly into the bush it would push the wheel forward, yeah. Unlikely to be an issue though as just driving the car normally will exert a lot of force on the control arm and help it remain properly seated.
If you didn't preload the bushes properly you may have damaged them, but if they'd torn completely then the control arm would more likely be sitting too far backwards (i.e. reducing castor) than forwards. Either way, get them checked out. At best they'll be adding a lot of spring rate to the front of the car, which in combination with the knackered dampers is going to feel horrendous.