Yes. The inner foam would become exposed and allow water to “sponge” it’s way into the board. It would gradually start rotting and becoming water logged and heavy.
If the board has removable fins there are locks you can attach to the fin box. Or you can get a couple of these tightening cable locks and attach them tightly on each side of the wide spot while connected to a longer cable lock so that they cannot be slid off.
Master Lock 8418D Python Keyed Cable Lock, 6 ft Long, Black https://www.amazon.com/dp/B0009V1WP2/ref=cm_sw_r_cp_api_i_VgifFbJTQWR2Y
You want an adjustable cable lock. Commonly used for bikes and ladders. Cable has lock attached on one side, and slides through the lock on the other side. When it's locked, it can only be tightened, not loosened. You'll have to find a size that fits, or increase the hole size.
Masterlock Python. You won't look any further. These aren't the bullshit micro locks that can be popped out with a jiggle. Under $13 on Amazon
It's only mentioned once, so I'll reiterate -- COVER YOUR BABY. Get a nice dirty cheap cover, and throw it over. This, in conjunction with your alarmed disk lock and a cable lock should alleviate your concerns, with time.
You want an adjustable cable lock. Commonly used for bikes and ladders. Cable has lock attached on one side, and slides through the lock on the other side. When it's locked, it can only be tightened, not loosened. You'll have to find a size that fits, or increase the hole size.
https://www.amazon.com/Master-Lock-Cable-Python-Adjustable/dp/B0009V1WP2
Edit: this might be thin enough, but you would also need a padlock:
https://www.amazon.com/Master-Lock-Steel-Cable-Lockout/dp/B0045Y0ONU
I use these. They work great.
Master Lock 8418D Python Cable Lock with Key, 1 Pack , 6' x 5/16" , Black https://www.amazon.com/dp/B0009V1WP2/ref=cm_sw_r_apan_glt_fabc_C8R12H6PZWPVB3P7VR3H?_encoding=UTF8&psc=1
I use one of these as an added line of defense.
Master Lock 8418D Python Cable Lock with Key, 1 Pack , 6' x 5/16" , Black https://www.amazon.com/dp/B0009V1WP2/ref=cm_sw_r_cp_api_glt_fabc_52G00AN2K3CBJEZ7WJ61