I'm sure this is done all the time and would be very successful. I know about the IUI part but I don't know anything about getting the sperm.
We used donor sperm because hubby has azoospermia secondary to undescended testicles. We got our sperm from Xytex and they were extremely professional. We bought 4 vials initially and after 5 cycles, 3 actually getting to insemination stage (2 abandoned) we conceived and now have a healthy, beautiful 1 year old. Our choice of donor was fab with Xytex - even though we are in the UK we chose to import sperm and couldn't be happier with the match of donor. Unfortunately we should have bought more vials originally as our donor didn't ever donate again so we have 2 vials (they had one left) if we choose to have a sibling for DD1. Have been advised IVF will give us a better chance of a sibling with the vials we have (its important for me that DD1 has a biologically 100% match).
My advice - take your time choosing a donor and think about the size of family you want prior to the initial IUI.
I'm hoping to have my first and hopefully last IUI using donor sperm in a couple of weeks. So as for now I can't share any personal experience about the IUI process. I have purchased the sperm, though. I recommend looking in the solo mum's thread and the Did you have a successful IUI thread - both under Assisted Conception.
I don't mind questions at all. I bought three vials from California Cryobank. They were 1 of 3 sperm banks on my list of possible banks to use but after meeting with my RE, California Cryobank was the only one of my list he worked with. Also because I live in LA, I can pick up the sperm instead of needing to have it shipped.
How I picked my donor?
I put together a selection committee made up of my friends. The committee was made up of a pediatrician, a social worker, a scientist, and a public health administrator. And they're all wonderfully fun, funny, and incredibly supportive of me. I'm going to be a single mother by choice.
I chose my donor by starting out with the basics: race, hair color, minimum height, etc. Then I looked at medical histories, read bios, and looked at baby pictures (for an additional fee you have access to baby photos). I came up with a potential list of 12 - 15 and then gave my list to my committee. They in turn narrowed it down to about 5 or 6, ranked them, and then of course I had the final say and I went with my gut. I know this sounds crazy but it was so much fun. It made a "strange" situation less strange.
This was probably more than you wanted to know but if you have any more questions please don't be afraid to ask.