Worse case:
If the antennas are close enough together, you can induce enough RF energy off the J-Pole transmitting antenna to get into the scanner antenna and down to the scanner. Turning the power off on the scanner does NOT disconnect the antenna from the soft/expensive bits inside the radio. Transmitting with your 2 meter radio, even with the scanner turned off, can still damage your scanner.
It might be rare, but it does happen, especially with consumer grade scanners.
Less than worse case:
Keying up your transceiver will cause enough RF energy to get into the front end of your scanner to disrupt reception. This is called receiver desene. While it may not damage anything, it'll keep you from receiving anything on your scanner while you are transmitting with the other radio.
Either way, you want a lot of separation between the two antennas.
If you do something like this, you ideally want quite a bit of vertical separation between the antennas if you are going to try to do this on the same mast. Either that, or quite a bit of horizontal separation, as in several feet at least.
You'd also do better if you used a higher grade cable than RG-59. That's pretty low end stuff and you'll lose some of your received signal just in cable losses before it can make it to your scanner. Use RG-6, specifically the RG-6 QS (Quad Shield) stuff if you are going to have both antennas on the same mast. It's also got less loss, so more signal will make it to your scanner.