Good question, and this is an interesting swap. Here is what you need to know:
Yes, the 3800 needs a PCM
The 1999 3800 Series II is a fully fuel-injected, computer-controlled engine. It absolutely requires its Powertrain Control Module (PCM) to run. Almost the entire engine wiring harness connects to or from the PCM, and the vast majority of sensors are engine-specific. The good news is that the engine and its PCM are largely self-supporting. You bring the engine, harness, and PCM over as a package and it functions as its own closed system, much like the LS family does.
The 4L60E is a different story
This is where it gets important: the 4L60E is electronically controlled for both shifting and line pressure. If you depart from the native engine/PCM configuration (meaning the factory Camaro PCM is no longer managing the trans), you will need a dedicated aftermarket transmission controller. Without one, you are stuck with reverse, 3rd gear only, and max line pressure. That is not a trail-friendly situation.
Aftermarket standalone trans controllers from companies like TCI, Bowler, or US Shift are the common solution here. They let you control shift points, line pressure, and TCC lockup independently of the engine PCM.
Compared to LS swaps
The concept is similar to LS swaps in that the PCM travels with the engine. The 3800 is not quite as well-supported by the standalone/tune community as the LS platform, but it is manageable. The Camaro application's PCM can often be simplified (VATS/security deleted, A/C and emissions stuff stripped out) by a tuner familiar with GM OBD-II systems.
From Novak
Novak does not offer a standalone PCM or transmission controller for this combination. Our catalog focuses on mechanical adapter kits and transfer case solutions. You will want to source your trans controller from one of the aftermarket specialists mentioned above.