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Will it work?
For a given definition of 'work' yes
When you pedal it will drive the rear wheel.
The chain pitch is the same (on all speeds) but the inner width are different between 8 speed and 9/10/11, but that just means the chain will be a bit wider than the teeth.
The outer plate widths are also different between 8/9/10/11 speed so shifting may be a bit iffy with the wider front mech cage, the pickup pins of the bigger rings might catch on the wider chain when running in the smaller rings and it also might overshift when shifting down as I think the inter-ring spacing is (slighty) different.
Any particular reason you can't us an 8speed chainset?
I'm reluctant to spend money on my commuter/winter bike (especially as the downtube is dented and probably on borrowed time) - therefore buying a nice new 11-speed Ultegra chains for my decent road bike and shifting the 105 from that to the commuter seems more palatable! Backwards logic maybe.
It's currently working fine with a 9-speed chainset - well, apart from the non-driveside arm constantly trying to fall off and hence the need for replacement.
I'm sure the classifieds or a local bike Jumble or if you have one a local Bike recycle project would turn up an 8 speed chainset (or rings) for peanuts. If you were local to Exeter I could probably sort you out with an entire chainset for < £10
EDIT - current one square taper or external bearing type? ie: is just replacing the damaged arm an option?
You can probably get a crank arm for a tenner.
Or a complete chainset for 30.
If you shop around and aren't fussy.
Or a complete chainset for 30
[url= http://www.sjscycles.co.uk/alloy-compact-double-square-taper-chainset-50-34t-175mm-prod31096/ ]Brand new, from an actual shop - £24.99[/url]
if you put a bit more effort in an find something in a deal or on ebay you could probably get under £20, and the above is not a bad chainset for the money, especially if it's just for commuting duty as steel rings will last for ages, and they're at least replaceable unlike horrible super cheap stamped/riveted chainsets. (assuming you need Sqaure Taper of course)
Hollowtech required. My commute is 30km each way, and it is also my winter bike, so don't really want to drop below Sora level. I can get Sora for just over £40, so not bad. Should probably just stump up a bit of cash, but as I said if I can upgrade both bikes in the process by switching the chainset over from my other bike then it would all seem a bit more palatable (despite costing more!).
TBH on a winter/commuting bike the endless rattling and clattering and never being quite right of an otherwise 8 speed driveline with an 11 speed chainset would drive me mad. My commute/winter bike was generally the bike I did the most miles on and spent the most hours on.
Until I stopped commuting by bike.
full Sora Chainset for £40 is probably a good option. The 3500 Sora is decent kit, just a bit heavier, but it's robust and reliable.
Steel rings (at least smaller middle one anyway) for winter and commuting will last waaay longer than Alu ones so for that if you want longevity it's actually better not to go above Sora level as Tiagra is the first point at which the middle/inner becomes Alu.
Big rings generally have enough teeth that the Alu ones wear acceptably anyway.