you can, and it is common practice in API manufacturing. The issue with NaOH (and with every harsh cleaning agent) is that the contamination is decomposed into contaminants that may be even more active or toxic than the original contamination, but may go undetected by the analytical method. In API production this may be no issue as the purification steps are designed to remove the degradants.
To detect NaOH i would perform a limit test with the pH of the rinsewater, or even the flame colour test. NaOH has as quite low toxicity (2000 mg/kg orally, rat) so most probably the limit calculated is relatively high.
i suppose you can use 2% Sodium Lauryl Sulfate, the question is what you want to clean. The "one fits all" solution is cumbersome and expensive. As a first approach, evaluate if what you want to clean is acidic (needs alkaline cleaner), alkaline (needs acidic cleaner), or neutral. If your product mix includes both acidic and alkaline substances, usually a neutral cleaner will do, but a lot of them get easily contaminated microbiologically. The most comprehensive way is to clean first with an alkaline cleaner, then with an acidic cleaner (ideally they should neutralize each other), and a final wash with a neutral cleaner, but this is usually a gross overkill. Take into account the cleaned materials (anodized aluminium as used in blister lines and tablet presses does not withstand alkaline cleaners) and environmental considerations.
If you need to use NaOH specifically, this in itself is not an efficient cleaner and it will be better if combined with a surfactant. One of the best on the market is from a company called STERIS and is called ProKlenz ONE.
Obviously the validation requirments will change slightly, but the surfactant in this product is HPLC detectable and will make the validation of its removal easier to monitor. in this case, TOC can also be used to assess the removal of both cleaning agent (which can't be done if only NaOH is used) and process residue. Obviously if you get a TOC signal that is above the threshold, you will then need to identify where it comes from, but basically, TOC from cleaning agent means your rinsing process is incomplete. If, however, the TOC comes from the process residues, your cleaning process needs to be optimised.