I suppose this would work, as long as there were always a moderator available to promptly approve legitimate posts. Requiring approval for the first post only would be good enough. But it wouldn't stop them from adding 50+ spam accounts per day.
This might work well in combination with the automatic deletion of accounts for which there has been no initial post within, say, 24 hours. The first message of the registration routine would be something like, "Registration is not required for viewing any part of this website, only for posting messages to the Forum. Please do not register unless you intend to post messages. New accounts for which no post is made within 24 hours will be deleted."
But I don't understand why any such measures are necessary. The other SMF 1.x forum I frequent is ten times as big and 100 times as active as this one. It's attacked in the same way, but has no measures like this. There are spam accounts in it's membership list, but only about one per day. Those ones are obvious spam accounts, suggesting they're not so few because the admins are deleting them. They must have measures that are effective in preventing most of them from registering.