grey water in hugelkultur?

Thoughts please on grey water in hugelkultur?  I have a long hugel on a slope (end to end) - bottom logs in a spade depth trench (in clay) with partially dammed sections to slow water. Excess drains out at bottom end.  I drain rainwater tanks into the hugel to keep things wet. It's about 3 years old now (I think) and rather neglected / overgrown with grass/weeds due to other priorities  - but should by now by nicely 'mature and alive' for when I get round to clearing it and planting veg again.  I'm building a temporary shower, sink, washing machine area ready for when we move onto the land and live in caravan whilst we build small passivhaus home.  So my question to myself is whether it's sensible to drain the grey water to the hugel? (ignoring any regs!).  I'm figuring yes as will be 'below growing medium' and the rotting wood bacteria etc will probably filter & treat water too before any excess comes out the other end(?). I also have a raised bed partial hugel which is my other option - on gentle slope. (wood was at ground level then a mix of old hay / horse manure / clay spoil).    I'm aware there are lots of opinions on using grey water generally, but would appreciate any thoughts please for this specific scenario.
many thanks

Seems like a good idea to me. It probably goes without saying grey water usage makes it all the more important to be using only biodegradable and non toxic products, but that would be my only major concern. The garden filtering out nutrients would also mitigate my other concern with grey water, which is its potentially being hard on wetland insects and fish due to the soaps and detergents. I might also avoid using it from above on leafy greens or on root vegetables, but that may be unwarranted and you seem to be wary of that already.

Our laundry runs into a gravel pathway that runs into the garden between hugels. I’ve intended to get the shower and sinks redirected to the same area, so thanks for the reminder to get on that as its our dry season and the garden can use it.

thanks Ben, much appreciated, a second opinion always good..........