I can think of several things that might go wrong. I cannot say if these things actually will happen:
1) Frequently opening the battery access lid may wear out the Velcro retainers on the lid, causing whatever issue the Velcro was supposed to resolve (rattles?) to start happening.
2) Resting objects on top of a battery may damage wires and/or cause short circuits (short circuiting a battery can be really bad). You have a lot of insulating materials between the wires and your clubs though, so maybe you are OK.
3) From the inside of the battery box there is no padding to the the right rear fender. If your bag and/or clubs should shift due to hard cornering (hard cornering in a Giulia? Who would do that?

) or bumps in the road you could end up with dents in your fender.
4) Even though the battery is ventilated there may be golf club attacking acid and/or extremely toxic lead salts around the battery.