If you can use something like JSON to post the info to the server at distribution centre then as kendash said it should be doable.
If you look as my PMS Intergration thread you will see that I am making good progress on scripts for posting sales data to the PMS System (cloud based)
I am working on an on demand post for charging to room accounts on PMS and daily post to transfer the remaining sales data so we can have one set of reports covering all revenue streams both rooms and epos.
Inventory wise I have not and am not going to be looking into as a product sales report is enough for our stocktaker and the PMS system doesn’t need to know inventory.
Either way this will give you an idea.
If your erp system can accept incoming formats supported by samba post scripts, JSON for example then between that and some jscript and likely some SQL you could send over virtually anything.
I now have have a pretty clear idea of the connections between orders, tickets, products and payments and feel I could (with bit of help sometimes) now pull pretty much any info sales related from samba using SQL.
If the inventory side is structured in a similarly logical way you should soon be able to get to grips with it.
Time wise would depends on your jscript and SQL abilities. Took me a while but was complete novice in regards both with only code experience being fairly basic HTML and css.