It certainly possible but it does have several challenges.
If you use http validation then all the servers that could respond for a particular domain have to either share the same filesystem (so the challenge file can be served up to Let’s Encrypt for validation) or you need to send all requests to /.well-known/acme-challenge to one server only.
If you use DNS validation (whereby you use DNS apis to create a TXT record with the challenge answer) then any machine can do the validation and certificate request (even a desktop).
In either case, Certificate deployment would require custom scripting (a post-request script) to copy (and name) the pfx where you need it, usually a Central Certificate Store like a UNC path. Alternatively you would custom script binding updates per server/site yourself.
We don’t currently provide any specialised functionality for load balanced sites but it may well be a feature eventually, some thought has gone into centrally orchestrating validation and deployment but only a little so far.