Not saying it will survive an entire Trump presidency, but I think it's not on the chopping block immediately. I do worry that they won't be able to expand as planned though to have mini-USDS people in each Agency because of the hiring freeze.
Here is his presentation: https://www.oreilly.com/ideas/two-years-of-the-us-digital-se...
Without that sort of personal investment from the president (or someone else very high up), I don't know how effective the USDS can be, even if it is funded. In my experience the main ingredient in organizational change is will, not technological know-how.
And again, the question is who in technology wants to be associated with a Trump administration. Even the tech-savvy Republicans I know cannot stand Trump. Maybe that will change as the reality sinks in.
18F is housed within GSA and so is somewhat isolated from political interference. That said, private contractors don't like it and will seek to label it as a wasteful project (already started--there was an attack article on HN last week).
The U.S. federal government under Obama had started to take some small steps toward modern digital competency. My expectation for a Trump administration is a complete reversal of that. Who's going to champion technology? Trump?? Mike Pence? Giuliani? And how many young talented developers are going to want to take a pay cut to eat bureaucratic shit in DC for Donald Trump? The allure for USDS was Obama himself.