As a disclaimer I've never worked on Di2. Having said that I volunteered at a shop and assembled a few bikes for them. The first bike I did was a Specialized Ruby road bike. It took me 3 hours of solid work to get it going. It was pre-assembled, yes, but pretty much everything was done at a marginal level. I had to redo a lot of stuff, give leeway for potential future fits (meaning cables had to be long enough for a crazy long stem with tons of spacers), and get it in such a shape that it wouldn't come back after a week because the cables stretched.

Previously I'd worked in bike shops for 15 years, managing for 6 of those and owning for 3 of those. I know how to wrench but I also understand the implications of having a job less than 100% done. If a shop assembles a new bike they're on the hook for that assembly. With repairs there's always the "well it was a pre-existing condition" when the fork fails and the rider faceplants at 40 mph. On a new bike assembly the shop needs to cover its butt.

Most shops need to make $65-75/hour on their mechanics to stay open. What's a flat fix cost? In my days it was enough to cover 9 minutes of labor. In that time a mechanic had to remove a wheel (if it's a rear you have to verify the brake and derailleur adjustment status so you don't get blamed for an improperly adjusted brake or derailleur), remove the tire/tube, check the tire for damage, check the rim and rim strip for damage/problems, install a new tube correctly so it doesn't blow out, reinstall the wheel, and make sure the brake (and derailleur if applicable) work at least as well as it did before.

At $65/hour, for 9 minutes, it's about $9.99. Suddenly $9.99 doesn't seem to bad for a flat fix, if that's what the shop charges.

If that's what the shop charges for a flat fix then $200 for a bike build is reasonable - that's 3 solid hours of work by one mechanic that has, say, 10 years experience minimum.

At the other end of the whole thing, meaning on the good side, you'd be able to get on the bike with some high level of confidence that the bike is going to be good.

Here's the thing. If your "friend" really wanted to do you a favor he'd have built the bike up and then broken it down for shipping. He'd have been able to do any warranty issues (what will you do if there's a crack in the frame under some decal? What if the derailleur hanger is a bit bent?), tension the wheels, adjust the derailleurs verify everything was working, and get you the bike in a real "I can put the bike together" state. By sending you a virgin bike he's sort of dropped you off in the middle of the wilderness. Equipped with food and such, yes, but still in the middle of the wilderness. If your "friend" had spent 4-5 hours assembling and then packing the bike you'd have been much better off.

The answer to your question is "If you have to ask then you should have it done by a shop". You can learn by doing it yourself and the Di2 shouldn't be weird for someone with more tech type knowledge, but you don't learn how to wrench a car by working on a Ferrari and that's what you have there. Have a shop do it and enjoy your very nice bike.

You'll probably want to make sure the bike fits too. That's a different discussion in itself.