Not really.

State level elections tend to shake out differently than federal elections. That's due, in part, to the fact that the state is gerrymandered in favor of Republicans at the state level. Republicans have also done well coasting off of Sununu's popularity. Democrats did manage to win the House/Senate in 2018, and narrowly lost the house this year (despite it being Republican favored). It's not like the Democrats haven't held the Governors mansion in the past 20 years. Lynch, Shaheen, and Hassan were Democratic governors. Republicans actually had a bit of a rocky time with their candidates up until Sununu.

If you look at federal election results, things are actually pretty dire for Republicans. You can see the results most strikingly in Hillsborough County which contains about 1/3rd of the state's population. Historically, Republicans have done well in suburbs around Manchester, but they've shifted pretty drastically leftward. Goffstown, Bedford, Hooksett, etc. All shifted ten points towards Democrats since 2016. The most striking results is Merrimack, which has shifted 15 points. It's emblematic of how much Republicans have lost in elections nationally. Derry, is also of note since it's pretty deep red and Democrats only lost it by about 2 points this year.

Also of note, Dover, which is one of the bluest cities in the state, has also shifted 15 points towards Democrats and had some of the highest turn out in the state this cycle. That's bleeding over to Rochester, formally a red stronghold, as residents from Portsmouth/Dover are priced out of Dover and move to Rochester. Rochester is pretty purple now which is kind of crazy.

I'm also not convinced that the NH Republicans, which seem to have zero idea of what an electable candidate looks like, won't nominate a Trump candidate for Governor and get blown out by a moderate. If you look at the candidates they've ran for our House and Senate elections, since 2018, they're all crazy people. The strongest people on their bench are like Gatsas and Edleblut, who are both terrible statewide candidates.