I wonder if there is a way I can insert a gene into the genome of a mouse embryo (using CRISPR for example) which then is only transcribed only if a certain pathway is active? Something like placing it at the same position as a gene in the pathway for example? (Excuse the layman terms, it's been a while since I studied these particular aspects of molecular bioloy).

You would put it  under a promotor that is active under the desired circumstances.