If it happened.
My bet is Alaska Libertarian Party membership would drop by 50% to 75% if the leadership pulled that move. There would also be an immediate move to oust the current leadership.
(My bet as a past LP county chair.)
It's happened before. The Libertarian Party of Illinois ran a Buchananite Republican as their nominee for Governor in 2002, just to get someone with name recognition. He was all for the war on drugs and made no bones about it when he was the Libertarian Party's candidate. Also he ran heavily on socially conservative issues that the LP tends to ignore.
Speaking of Buchanan, Pat Buchanan himself took over Ross Perot's old Reform Party in 2000. And certainly Buchanan's politics are pretty far removed from Perot's. He succeeded in getting his loyalists to take over key party posts and nomination him -- though the Reform Party erupted into a civil war after the 2000 election and eventually faded into nothingness.