Congratulations on your decision to buy a new home!
If you are planning to buy a condo, the project which the condo is a part of must be approved, regardless of the down payment being made. If you are planning to go with an FHA loan (which is advisable if you are putting less than 20% down), then you can get a spot approval, as you mentioned. If you can put at least 10% down, and want to pursue conventional, Fannie Mae financing, then the project must be approved by the bank that you are taking the loan out with. Once upon a time, Fannie Mae approval was all that was needed. In today's market, the physical lender will want to approve the condo project personally.
First, let me give you the big picture. The lenders, FHA or otherwise, are concerned with protecting their collateral...which is the condo you wish to buy. Since condos are part of a HOA, the lender is very concerned with the HOA and the project, and how it is run. Here are a few things of the many things that can make a lender not approve a condo project:
a) More than 15% of the HOA dues are deliquent
b) More than 51% of the units are being occupied by renters rahter than the owners
c) There is pending litigation against the HOA
d) There is not adequate reserves available to perform unexpected, but necessary repairs
So first, decide on what type of financing makes the most sense for you and get lender pre-approved. Second, find a condo you wish to purchase. Third, let your lender do the work to discover if the condo project is approved, or will be approved by the lender. And just know that if the lender does not approve the condo project, they are doing you a favor by discovering deficiencies in your property that would eventually effect your future property value. If the lender will not approve the project, you probably do not want to buy into that proect anyway.