What are the chances Skoda will have your part in stock for same day pickup or do they have to order everything from the main Skoda warehouse?

Depends what it is...

 

I'd expect them to hold stock of popular items. If it's something more uncommon it might be in a national warehouse. The rarest/most unusual items will probably come from Germany or the Czech Republic.

TPS are more likely to have what you need. TPS - Home page

Supposedly only sell to trade customers but "if you don't ask, you do don't get" tends to apply.