Answer: No
Explanation:
The statute has already conferred the powers to both select a site for and to construct a monument on a federal agency which by extension is the Executive branch. The Executive should therefore have final say in the monument's location and design to enable them break ground as soon as the necessary funds have been appropriated.
To still include a provision that the funds may not be expended until both houses of Congress have given further approval amounts to interference with an executive function rendering it unconstitutional as the powers of the Executive and the Legislative are to be separated.