It is an interesting question ... one about which I know little.

This forum has had pictures of LPG tanks with grounding electrodes attached. I know not the reason - gas code is not one I'm familiar with - but it seems to be a common practice .... especially where there is any chance voltages will be induced by overhead lines, radio towers, etc.

It's also not impossible that the rod seen being driven was a sacrificial anode.

If it is meant for grounding, I see no harm in also tying it to the household ground net. Yet, without there actually being power at this detached tank, I'm not sure you're required to connect it.