If your ISP is not providing primary or secondary DNS services for your zones, then no.
The world knows about your changes when you go to the registrar and change the NS records to identify the new authoritative servers.
When queries are made and the host information is not known locally, it traverses up the tree to the root servers which query the top level domain for the name servers responsible.
The real problem lies with the individual records within a zone and the time they are set to expire. If all records in your zones are the same and you are simply changing the NS records at the registrar and your hosting provider is setup in advance with your zone information, then you should be good to go.
I've moved DNS a lot. I typically keep the old DNS server in production for 15-30 days as a matter of principle (lots of times I'm also changing record information, though).