I have a few issues with this.
First off duct tape's adhesive has a rather strong smell... Not something I want around my tubs
I agree that the chances of the snake getting stuck are very low as long as it is on the outside... But there is still a chance.
There are much better ways to black out a tub that have 0 chance of negative situations. Plus duct tape makes a terrible mess so that is another thing to consider.
So to be clear, I'm not saying that I think that there is any immediate danger but this really isn't the best idea overall.