You can stabilize mechanum drive with a gyro without a whole lot of trouble, but, as previously stated, handling still suffers even though your robot won't drift when strafing, since you're using more motor power to make the robot not drift.
Also, the year before I joined our team (2005) our
tetra robot had mechanum wheels but the software was never written to make it work like it should. So, that year the left two motors were paired to the left joystick, the right two to the right. Our driver that year said it was the best robot to drive he'd ever had, since it could powerslide really really well.
Just something to consider.
From personal driving experience with our robot interacting with other mechanum drive robots, i've found them very easy to push out of the way and if another is trying to push/disturb our robot, it's almost not noticeable after the initial impact. Even in second gear our robot this year has been able to (so far) push most mechanum robots without much issue.
-q