Yes. Desktop applications can be just as quick to develop and iterate on as web based ones. Slapping together a winforms UI in visual studio is still the quickest way to get to MVP status.
A better solution would be something like chocolatey (https://chocolatey.org/), which is basically a package manager for windows. It doesn't do the automatic updating, but doing that with a remote powershell script should be doable.
For some perspective though, if you automate this as part of a CI builds it should be a once off cost, it's not a justification to make something a web app instead.
Managing updates to a cluster of backend servers is at least as difficult, because they usually have shared state (a database).
Having a desktop application doesn't mean you can't/shouldn't have a web application. It also doesn't mean they need to look/behave exactly the same.