The long technical answer here leaves out several huge factors.

Polarization -- typically in this type of setup, you'd have the yagi horizontally polarized and the j-pole vertically polarized. This significantly reduces interactions between the two.

Radiation pattern -- Again, in the typical arrangement, these two antennas would mutually be in each other's null direction which would significantly reduce their interaction.

However, they two antennas would be in each other's near field where polarization and the radiation pattern are less settled.

The typical amateur radio way to find out is to set it up and test. It sounds like you will be putting two radios on these antennas anyway -- connect them both, transmit on one, and see if that signal gives the other radio front end overload. Start at low power first.

The long technical answer here leaves out several huge factors.

Polarization -- typically in this type of setup, you'd have the yagi horizontally polarized and the j-pole vertically polarized. This significantly reduces interactions between the two.

Radiation pattern -- Again, in the typical arrangement, these two antennas would mutually be in each other's null direction which would significantly reduce their interaction.

However, the two antennas would be in each other's near field where polarization and the radiation pattern are less settled.

The typical amateur radio way to find out is to set it up and test. It sounds like you will be putting two radios on these antennas anyway -- connect them both, transmit on one, and see if that signal gives the other radio front end overload. Start at low power first.