I am a Homestart volunteer and a mum of twins. Most of the families I have supported in the last 10 years have had twins (or triplets).
Contrary to what PiedPiper says, I have done the following (often);
Helped with housework, usually alongside mum whilst new babies slept (a messy/dirty house can be a huge cause of stress). I've often done a pile of ironing whilst mum and twins slept.
Looked after babies whilst mum went out to GP appt, physio appt, or just to the supermarket.
Taken babies/toddlers out in buggy/to the park so mum has some time to herself.
As far as I'm aware I've broken no rules, indeed all these activities have been reported to my area organiser via my diary sheets.
My guess is that mum's are told that volunteers don't do housework/babysit because there are some people who would abuse this situation. As far as I'm concerned my role is to support the family by mucking in and doing what ever helps to relieve stress and worry, be that tackling a pile of dirty dishes, or having a long chat over a cup of tea.
Janberry, I suggest you play it by ear. Wait to meet your volunteer and then be as open as possible about the ways she can support you (these will of course change as your babies get bigger).
Good luck with the rest of your pregnancy, and I hope the Homestart "experience" is helpful for you.