It looks like you're new here. If you want to get involved, click one of these buttons!
If mod_rewrite is not enabled, will Sendy still be able to work, or will it be completely broken? Perhaps it's a halfway house and only some aspects will be broken?
mod_rewrite usually cannot be detected if you're on shared hosting but is indeed enabled.
I just visited your installation and I can access /login without any problems. That means mod_rewrite is enabled on your server. If it is not enabled, you'll get a 404 error when accessing pages without appending .php at the back.