You may still get an exception hold on the transfer if all of the named account holders on the checking and savings do not match. In my time in banking such an internal hold was exceedingly rare but did occur if other red flags were present.
Usually a hold is not an issue when transferring to savings.
Further, regardless of the factors above, your institution may require you to complete the transfer with a teller rather than digitally, but that's the institution's choice.
Side note about large transfers: When you're doing an internal transfer of $100,000.00 or more, even if named account holders match, some banks' back-end systems will only process this amount in one day as a wire. If so, they will likely waive the wire fee.