Yes, your spousal visa is the one that allows you to work.
So it works like this:
1. Get an 'entry clearance' visa (ie, a fiancee visa which does *not* allow you to work) from the US
2. Come to the UK
3. Get married
4. Send in documents or visit the Home Office in Croydon to get your Further Leave to Remain (FLR) or spousal visa which allows you to work
5. After 2 years, send in more documents or go back to Croydon to get your Indefinite Leave to Remain (ILR) which again allows you to work, come and go in and out of the UK as much as you want, and to stay indefinitely.
Then after three years, you can apply for citizenship and a British passport. But that's another board entirely!
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Hope that helps!