I want to make a béchamel sauce with coconut cream instead of milk. Does anybody have a guess whether this will work?
First, you don't specify if you mean cream of coconut, or coconut milk. I think coconut milk would be the thing to try here, as it has less fat.
Second, if it works, it won't be bechamel any more. But this is a technical detail: if it is tasty to you, you should be able to use it as a substitution practically everywhere.
Third, does it work? I haven't tried it, but I would strongly assume that it will. Coconut milk has more fat than normal milk, but this isn't a terrible problem for roux-based sauces. Indeed, I have read recipes (in reliable cookbooks) which direct the cook to add melted butter to the roux before or after adding the liquid. Which means that the fat ratio in the sauce isn't too exact; it is the ratio of flour to water which you have to keep straight.
The one thing to pay attention to is that coconut fat melts around 34-35°C. So your coconut roux sauce will exhibit noticeable difference in thickness depending on the temperature. As long as you serve it warm, it will be a similar thickness to bechamel. If you let it go cold, it will probably thicken quite a bit. If you plan to serve it cold, adjust the flour amount accordingly.
I make a coconut curry "béchamel" sauce every once in a while. Usually use it with chicken and broccoli and etc. recipes that I serve over pineapple fried rice. Make a roux (using at least some butter), shake up a can of coconut milk and whisk it in until the desired consistency (and then I also add curry to taste). FYI: Béchamel sauces aren't served cold regardless of how much the flour is adjusted. They're béchamel sauces, not pudding.