Your question is worded in a confusing manner. If you are recording to tape, why on earth would you be using converters?
So perhaps one should assume that you were using the word "tape" euphemistically, and you are really recording to some digital medium, which for the sake of discussion, we'll refer to as a DAW. (Although obviously there are still some ADATs and similar thing floating around that are digital and use "tape").
Assuming we are talking about an analog compressor, if you do it after the converters, you will have this chain:
Mic --- Preamp ---- Converter --- DAW --- Converter --- Compressor --- Converter --- DAW.
As opposed to:
Mic --- Preamp --- Compressor --- Converter --- DAW.
A you can see, you are comparing one trip through converters versus three trips. In an audio chain, almost invariably, less is more.