I absolutely suggest that you DO NOT do this! The Arturia Rackbrute P/S has a capacity of 1500 mA on its +12V rail. Each AIRA module has a draw of 450 mA under normal operation, and a momentary higher draw on power-up due to inrush factors. And the System-1m has a draw of 800 mA! Plug in two AIRAs and a 1m, or all of your AIRAs at the same time, and you're running a very real risk of trashing the Arturia P/S!
The power draws of the AIRA modules are one of the big reasons they never got much traction with the Eurorack community. Why would anyone drop one of these into a typical build where you might only have 1000 mA to play with on the +12v rail, where a typical Eurorack module has a draw closer to maybe 40-50 mA. One AIRA module would equal the draw of perhaps ten or so normal Eurorack modules!
Leave these things in their cases and on their own power supplies where they belong. And this should be a lesson: just because something fits in a Eurorack cab does not mean it belongs in one. Also, size isn't the only important thing in modular synths...current draw is perhaps as, if not more, important, because if you pop your power supply and it doesn't simply stop working altogether, you might get all sorts of electrical havoc for a fraction of a second that could spell the end of your entire system.