Great question. As @rob_marshall mentioned in an earlier post you can certainly run a process from Informatica.
I'm wondering if this might be your issue: make sure that when you create the import action (or export action) that you save the action as "EVERYONE". If you don't, Anaplan won't find the file.
See if that helps.
One last observation. Delete and Insert is a very heavy processing solution because the delete action will turn on the logging. Highly recommend you UPSERT if you can. Use audting modules to weed out the records you no longer need. Your processing will be much faster.