With caution, yes. It is called "gray water", and I would avoid watering sensitive plants like rhododendrons, camellias, begonias, and ferns with it. It will be important to use all biodegradable washing up products. I would also flood the plants you use it on several times a year with clean tap water, to help the rain in removing chemical buildup. Don't use sewage from the toilets for this.

With Tugb. provisos above yes. But do make sure that you are using biodegradable products. Same applies to bath water.