Yes, this is a good first step. The appropriations bill has to pass every year so a pro-4th amendment coalition can exert leverage by threatening to block the bill if the programs are not de-funded
Stripping the authorization for the programs would be the next step but that is more complicated because it requires a separate bill, which is harder to pass and gives congressional leaders more opportunities to quash it. Otherwise you have to wait for the renewal of the PATRIOT act to block it.
Repealing the authorization is possible with enough support but it will take longer than simply de-funding the programs.