Yes, as long as there is no salt, butter, etc.

I think cooking water comes under the term 'grey water', which is water you wouldn't want to drink, but actually doesn't have anything more human-sickening than soap in it. Your plants just might think you are giving them a treat, since most cooking water will have traces (and thus nutrients) of the vegs that had been cooked.

If you aren't already, switch to using soap (not detergent) for washing everything including dishes and people; a mild solution of white vinegar is an excellent rinse for soapy items. The used wash and rinse waters are quite satifactory for gardens -- remember that soapy water is an OG treatment to get rid of bugs in the garden.