It used to be possible and not extremely difficult to put cards into OCTGN and play with them, but that went way beyond my capability a long time ago. I'm sure there's a program online that allows it, but I'm not familiar with it if there is.
I think what you're working for would be a lot of work for Alex, but I do agree that it would be appreciated.

It's absolutely something I'd love to do. "Building decks" is Stage 1 of the three-part plan I mentioned over at Draft Feature, where Stage 2 is "Drafting" and Stage 3 is "Gameplay".

Stage 1, Decklists, will likely happen at some point. I've done a lot of planning for it - I've got fairly detailed design specifications of the feature, and the architecture and user interface to it all. I've got some early prototypes in development at home. It's hard to find time to work on Multiverse at the moment, so I can't give you an ETA (it's not going to be less than a couple of months at least), but it's quite likely to happen at some point.

Stage 2, Drafting, is being developed as a separate website, Multidraft, by Chowlett, with occasional contributions from me. Multidraft can already generate boosters from any set here on Multiverse, and Chowlett has reasonably detailed plans of the various steps along the way to letting multiple players draft an arbitrary set.

Stage 3, providing a virtual gaming table to play our custom cardsets on, definitely has to come after Stage 1 and probably will come after Stage 2. I'm aware it's a lot of work and haven't made detailed specifications yet.

Is multidraft currently online or not yet?

It's online, at http://app-multidraft.rhcloud.com/ . But like I say, at the moment all it can do is generate boosters. The developer (Chowlett) has been putting his time into working on his online Dominion server instead. I will be working with him on Multidraft at some point in the future (probably this autumn) though.