Can I run my sink & disposal into my basement's sewage pump?
I see no reason why you can't run the kitchen drain into the basement bath ejector pump basin.  You will have to get the kitchen drain dumped into the ejector basin in a sanitary fashion.  The pump will cycle more often. You will probably shorten the life of the pump a bit.  If the pump is designed to handle the effluent from the basement bath it surely can handle a kitchen sink and dishwasher.
I would prefer this to a regular visit from the rooter man.