I would not attempt that.
Couple reasons:
First, if your 1.6L is the early one, the headgaskets are hard to keep bolted down already. If it is the later one, that is better, but still not ideal
If you get an even later 1.6L, the hydraulic one, you can at least upgrade to the MLS headgasket from an AAZ engine.
However, the factory 1.6L turbo engines had a far more turbo-friendly compression ratio (different pistons) as well as piston cooling jets and an oil cooler (your current engine has none of those items).
You would be better off finding a factory turbo 1.6L, but these were not super common even when new. They were only found in some Audi 4000s, Quantums, a handful of later A1 Rabbits and Jettas, and a handful of early A2 Jettas. I think the whole model year span was something like 1983 to 1986. The ECOdiesel Jetta, which came out mid-91 through 92, was also a turbo, but a very light pressure low emission unit with only a wee bit (7) more HP than the non-turbo version.
Once you realize how unobtainium those early TDs are, not to mention parts for them (as well as parts for the NA version for that matter) are quickly going away or are already gone, you may consider just converting it to a TDI engine. These are more readily available, the early TDIs (B4 Passat, A3 Jetta) are the same engine family as what you have, so they will bolt right in, and those engines easily outlast the rust-prone A3 bodies. You can also convert them to "M-TDI" meaning to run without any electronic controls if you wish. They are a simple wastegated turbo (the VNT is not) so can be easily controlled by what is already there.