Programming is very useful in the process of conjecturing, and to some extent even in proofs.
Here are some examples from my own research, in theoretical computer science and combinatorics:
An algorithm for maximum coverage (a basic combinatorial optimization problem) employs a non-standard objective function, with finely tuned parameters. These parameters ...
The only thing that programming can do for you is teach you logical thinking, if you have problems there.
The computer won't let you use assumptions or take shortcuts. You have to create a complete, logical sequence of instructions to get from the problem to the solution. And that skill is of course also needed for mathematical proofs.
This is pretty much in the realm of opinion, but as a math PhD and a long time CS professor, I'd guess the answer is no. Programming is fun and programming can be useful, but its application to proving theorems in mathematics is very specialized and a bit limited. And it generally doesn't apply to the sorts of things a struggling math student wants to learn.