Yes. The loan is for the total cost. $2000/month will get you low to mid 300s without buying down right? That’s what you can’t go over.
Most renovations will be under 100k and closer to 50k depending on the size of the house and the quality of hardware. It can be deceiving just looking at online listings. A flipped house selling for $150k more than it was purchased for prior to flipping probably only had 50-80k worth of work done.
Don’t forget that taxes and insurance are also included in the $2,000 maximum payment. after subtracting those, the remainder could in theory be used for renovation. However, also remember that your total loan cannot be more than 110% of the post-renovation value of the home and must still fit within your affordability. Unless it is a total gut rehab, it’s extremely unlikely you would actually use the whole amount.