As I ask myself the question and start thinking about it, I realise it might be obvious that it is worth it. But I thought I'd ask anyway as someone might have a nice analysis to share.
The other day, I cleaned a lightweight plastic bag (I don't usually do it, I put them in the bin when they are filthy) and thought it was a lot of water for a small single-use bag. It got me thinking: is the amount of water I used to clean that bag (I'd say about one litre) more than the water used for its manufacture and transport? Looking at both a recycled bag and one made from fossil raw materials would be great.