This theory is not supported by history. After the very moderate Republican Gerald Ford had been president, conservatives in the GOP took charge and nominated Ronald Reagan, who steered the party in a very rightward direction. George H.W. Bush was also considered by true believers to be too moderate, and he was challenged and politically damaged by a conservative in the 92 primaries, which arguably significantly contributed to his re-election defeat. Two years later, conservatives came back with a vengeance in the 94 congressional elections which saw the ascendancy of Newt Gingrich as the party's leader.
All indications are that when the party veers too far to the left or center, conservatives will usually end up pulling it right back. And in California, the conservatives are still very powerful within the party, as we saw in the 2002 primaries that produced the nomination of conservative Bill Simon over liberal Richard Riordan, who had been the early favorite.
If anything, it is Arnold who should worry. If he governs as a liberal, he can expect a massive conservative backlash that will again pull the party to the right and make nominating moderates even more difficult than it is now.
Whistling past the graveyard. The truth is that if the "true conservatives" lose the governorship to an incumbent with a 30% approval rating twice in 2 years "true conservatives" will be lucky to be allowed to bus the tables at the next GOP convention.