Firstly, IANAL/IANYL, and I will assume for the purposes of this answer that the FSF's attitude to what constitutes a derivative work is the correct one.
If Magick.NET invokes ghostscript solely through userspace, the resulting combination of the two doesn't become a derivative work of both; the two programs are "merely aggregated" and may be distributed together without either's licence requirements affecting the other. If ghostscript is invoked through a library, or some other shared-data-structure method, then the resulting combination of the two is a derivative work of both, and if distributed with ghostscript this derivative work would also have to be under AGPL.
What makes me suspicious that the latter is true is that Magick.NET themselves don't distribute ghostscript with their code, but instead require the user to download it. If they were confident that their use of ghostscript was mere-aggregation, they would not need to do that.
Assuming from that (and it is another assumption) that Magick.NET uses ghostscript in such a way as to make a derivative work, distributing ghostscript with it would require that the entire resulting derivative work was covered by AGPL3.
Whether that requirement extends to your product depends similarly on how it uses Magick.NET. If you are making some kind of derivative work, then the AGPL licensing requirement would extend yet further, to your code.