I've done all this, got myself membership then realised I can't persuade them to join me as I'm presently either doing yes man or house... so if I want to remain in the BoS I have to overthrow house, even though I actually think he'll probably make a good leader. D'oh.
Or is there a way round this? (or am I going to have to check in with yes man?)
I screwed myself over like this, too; I reflexively told Yes Man to ignore them, not realizing it might be possible to negotiate. I also completed their questline fully before House told me to blow them up. This resulted in a bizarre situation where I could tell House both that I had made the Brotherhood agree to help NCR, or that I had gotten the Brotherhood to attack NCR when the dam battle started, one after the other. However, I never actually talked to anyone in the Brotherhood to determine these things.
I think having Yes Man ignore them and completing the BoS questline prematurely screwed me over, but tbh I'm really not sure. I'd love to find out how I can get them to show up at the dam battle supporting the NCR. The only way I can think of so far is asking the NCR ambassador about it when he gives you the mission. However, the GECK does contain a possibility for convincing House that the Brotherhood could be useful against the NCR, so who knows.