I think the Bloodwretch can only be used with the Dreamer giving Fast as it's Rage Builds is only in effect for the "remainder of this activation". If you activate with something like Obey, it would cease to be in effect at the end of Zoraida's [or other master crew manipulator] activation and thus not be in effect when the Bloodwretch activates. Or it could even be that the Obey is a single activation of itself and therefore adds Rage Builds and then immediately drops it. Going by RAW on the cards, it says "this activation", so I'd think it would apply for that entire activation and not just the part of the activation which caused the 'wretch to Rage Builds.
You could subsequently use another of the manipulator's AP to earn some cards from a Bloodwretch, but that's slightly different to tagging a 'wretch with the ability to earn cards later in the turn. Also, if this were the plan, you'd effectively be using your non-Dreamer master's AP to proxy into a lesser model because: cards. 1 Dreamer AP for a net gain of 2 cards over 2 'wretch attacks and flexible activation to boot, reasonable imho. 2 non Dreamer master AP for a likely net gain of 1 card, not worth it. Zoraida with Powerful Control might be able to even this out a little more favourably with potential gain of 2 cards for 2 Z AP for Rage Builds and a bonus charge off a double mask Obey, but they don't cut it when comparing against Dreamer dropping Fast and forgetting about it until you're ready to activate the 'wretch.
I might have missed something, but I think the Bloodwretch card has specifically mentioned it's duration wrt Rage Builds which means it doesn't carry over in the way a typical set up would (like Dreamer's "Playtime" for example)