Would this likely do what I want it to?
It depends - you didn't say at what
distance. Depends upon distance, primarily, but also the caliber of holes, ambient lighting conditions, target type, and your own eyesight level.
But generally, yes, at 100 yards maximum, if that's what you're shooting at, a relative cheapie spotter will spot holes under average conditions; no problem.
However, it pays to step up in quality when you go to 150, 200, 300, and 400 yards, because at some point in there (between 100 and 250 yards, let's say), the cheapies will no longer resolve the holes for you, depending on all the conditions.
Is it normally cloudy or sunny when you're shooting? Is the sun usually "at your back" shining on the targets, or shining from behind the targets or from the side, based on how your range is set up?
Are you gonna use Dirty Bird or similar targets, or regular paper ones? White, black, or orange/color paper?
What's the max budget? Alpen, Konus, Brunton, Celestron Mak-Cass's, certain Leupolds, and certain Bushnells have a reputation for having a high optical-quality-to-cost value ratio,
on the low end (under $200-$250) of spotter prices.
You're gonna get vastly increasing returns on your purchase price going up over $25 dollars and not start getting diminishing returns until the $200-$300 price range. So, can you go to $50? $75? $100? $125? $150? More? If so, you may be very glad you did down the road if deciding to shoot past 100 yards, or on a cloudy day, etc. You are going to get what you pay for generally, particularly in this low-end price range. What's the max possible budget you can go, and I'd bet you can find a lot better scope than that one if you can bump up past $25.
Don't forget, optical quality (glass grind & coatings), objective lens size, and magnification all help in resolution the higher you go - in that order, generally.
My recommendation for a small, handy, cheap spotter, giving good resolution, under $100 (IF you're not gonna bang it around. since it's a relatively-more-fragile reflector, not a refractor), is the
Celestron C65 Mini-Mak:
http://www.opticsplanet.net/celestron-c65-mini-mak-spotting-scope.html
But better yet, if possible, step up to the Celestron C90 Mak, at right around $200:
http://www.opticsplanet.net/celestron-c90-mak-spotting-scope-bcbab.html
Give us a realistic max budget (if more than $25), and we can narrow it down much better.