I posted this over on HI board, but I'll cross post it here too.
No, you can't put a pool in a drainage easement. Yes, you can maybe bootleg it and get away with it, but it's a bad idea.
I've worked as a civil engineer on multiple projects that included putting new ditches/pipes/forcemains in drainage easements. There's some difference between "private" and "public" for those.
- Public is the City/County/State, or whoever those guys give the rights to. Can be an HOA or a MUD or even a for-profit company, as long as the municipality gives them rights. Can also be you, or your neighbor.
- Private is a limited number of parties, usually defined in the HOA docs, CCR's, or deed restrictions. However, if your HOA signs power of attorney docs with the City to allow the City to install some new drainage feature, it can also be the City.
So...... even though that's a private drainage easement, it can become public without your permission. If it's a public drainage easement, and the "public" decides to put some piece of infrastructure there, they will remove/demolish your pool, without your permission. They may not even notify you in advance. Hell, they may send you a bill for the increased cost of removing your property from their easement. You have no real recourse in that scenario. Sure, sue em - you'll just lose.
I worked on a drainage project (two 10'wide by 8' tall box culverts, 2 miles long) through an affluent neighborhood in the greater Houston area. There was one ~2,000 foot long stretch where we were going through a platted 50' wide drainage easement in the rear of houses worth >$2M, including a state senator. Several of the houses had garages that had been illegally built into the drainage easement. The contractor used a saws-all to cut the garages off at the easement line, and stacked the wood/shingles/concrete neatly on the owners property. Several sued, and all of them lost.
Even if there's never any drainage project that goes into the easement, it will still be flagged as a "encroachment" on any survey and it will hurt the resale value of your home. With that all said, you'll have to decide what % chance you think that the drainage easement ever gets used vs the value of a pool vs the danger of an encroachment hurting your resale value. Maybe you can get away with it.