My Aikido Sensei Jason DeLucia is also a UFC and Pancrase fighter, and firmly believes we should train in groundwork not just standing Aikido. We train in Aikido and Pancrase Hybrid JuJitsu, so we learn lots of BJJ techniques and do lots of suwariwaza. Whenever possible, Sensei works and has us aim to work from suwari instead of working BJJ techniques, keeping more upright. He's got some training clips on aikidog.com that will give you something of an idea.
Our dojo has serious students in it, not hot-headed kids. As for women doing groundwork, I've been training with Sensei for about a year and a half and have been grappling all along. I think it's a very important skill, and would hate to think of what might happen if I ever got attacked and didn't know how to handle myself on the ground. Besides the assorted-sized guys in class (all bigger than me so it's quite a challenge), one of my current partners is a policewoman who knows she lacks groundwork and wants to fill in that gap to keep safe.
Here's a clip showing Sensei getting out of a common BJJ position:
Pardon the camera work at the start of this one; it was hard for the cameraman to get into position so it moves around at first. It settles down so you can really see what's happening. Sensei is using suwariwaza in a situation police asked about because it's so common: