memcached?

Does DH care if people use/run it? Do people have experience running it on DH?

I don't know what memcached is, but you can do almost anything you like as long as you stick to two simple rules:
1) it must be legal
2) it must not use too many CPU resources (since you're sharing with others)
You can always send a message to sales@ if you aren't a customer yet, or submit a support ticket if you're already a customer.

memcache is a distributed memory caching system.

I don't see there being any real problems with running it for a small scale site. But if you have a need for memcache in the first place, then maybe you need to be looking into a dedicated hosting service.

memcache is by design intended to be distributed. meaning spread out over more than one source(in this case a server). There is really no point in using it for a single shared hosting account.

The thing with memcached is that it is a server running in the background among preferabally multiple servers. Hence the distributed part. There is a suggestion already for a memcached server.