Primary & Secondary DNS question

[Boris]

We just got a T1 installed.
We like to be able to manage our DNS but not having to worry about having it
up 24/7.
We were thinking on having our ISP DNS as secondary , pulling info from our
primary DNS
But registering our ISP DNS to internic as the one to use for our domain.
This way if our DNS goes down, the only effect will be that our ISP won't be
able to update anything until it goes back up, but everybody will still be
able to resolve names.
Is this correct?
Is this the way to implement?

Thanks