Yes and no. Mainly it's Chychrun's play that should give them hesitancy to sign him to a big, long-term contract.
Here's my thinking: Hutson gives them leverage to get a good (and tradable) contract for Chychrun. If Chyrchrun was playing like Quinn Hughes (or even prime Carlson), it wouldn't matter what Hutson was doing in college. But since it's realistic that Hutson may outplay Chychrun, the Caps "need" to sign a fair contract so that they can trade Chychrun if Hutson ends up better. So basically it has to be a contract that is tradable when his shooting % drops back to normal levels.
Apparently Allen Walsh has said stuff about players going for shorter contracts with the rising cap. If Chychrun were willing to do that, I wouldn't mind seeing the Caps give him 2-3x$10 million or something with essentially no trade protection on the second (and third) year. But historically, hockey players have favored longer contracts at lower AAV. (As would I if I were in their shoes.)