Core component of SQL Server for storing, processing, and securing data
What you have in mind is very bold and ambitious. And, quite likely, overly ambitious. It would be very challenging to get that going, and for the investment to pay back, the cost for performance regression in production must be very high.
Running performance tests on every checkin is very difficult. You cannot run your full test suite, but how do you know what tests you should run? A little more reasonable approach is to set up a full performance test that you run maybe once very 24 hours or so. Composing such a test is still anything but trivial. Exactly how complex depends on your system. The more functionality your system provides, the more challenging it will be. Probably, you should identify the core functions and start there. Then you can add things as you move on (and you get burned by performance regressions in production).
It's important to understand what while such a performance-test environment will catch some performance regressions before they reach production, they will not catch all, even if you have that specific stored procedure in your test suite. Keep in mind that SQL Server, like all other major RDBMS, has a cost-based optimiser that estimates which is the best plan from statistics sampled about the data. The statistics in your perf-test environment may differ from production, or there may be other differences which results in different plans with widely different performance.
And speaking of that, ideally, the perf-test environment should be a copy of production. But your production database may have very sensitive data, which makes it impermissible to have an unmasked copy in a test environment. There are tools for masking data, but that will also affect statistics, which increases the risk for that the perf-test environments yields different plans from production.