Let us know how you make out.
First the house after the pool was installed would need to appraise as if you had purchased a home with a pool. If we assume a existing pool adds $15,000 to the value of a resale house, and a new pool cost $35,000, you would need to contribute an extra $20,000 in cash at closing to get the loan. I am currently unaware of any loan programs that let you add a pool when buying a home. Does anyone else know of any?
In this case you might be better off taking out a separate pool loan after closing if you qualify.
I am currently working on a house purchase where the buyer is doing a conventional loan and has 20% for a down payment . We are exploring only putting down 5% and then after closing using the remaining 15% to buy the pool with cash. If you are tight on cash this wont work.
See link below for details of the FHA 203K.