It may, it may not. Incumbents are usually hard to get out of office, and once you put a liberal in office they have many ways to consolidate their power, and they won't take responsibility for their own failings, they will of course blame it on the RINO they replaced for a while and then others when that no longer works.
If the conservatives in the Republican Party let RINOs lose, the party leadership doesn't usually change it's approach, it starts saying that in order to beat the Democrat that now holds the office they need to run a "moderate" Republican that can appeal to more swing voters and pull them away from the incumbent Democrat.
Here in Ohio, the RINOs are in control of the party leadership. They have the votes within the party to set the party's agenda and to use the party's power to support other RINOs.
Those RINOs aren't going to relinquish that leadership just because they might lose a few of their members. Those in control are likely secure in their positions and would rather rule the minority party than be an outsider in the majority party.
To uproot them from the party leadership, you need to either allow so many RINOs to lose that you give the liberals tremendous power over your government for a very long time, or you need to vote them out in the primaries.
You want to scare RINOs. Tell them you vote in every primary election and you vote for party committee member positions as well.
They will relinquish leadership if voted out of office.
The Republican party will run conservative candidates in most of the nation if it realize that only conservatives are acceptable to the base and can get elected to office.
Republicans largely advanced a liberal, big-government agenda for the six years they were in charge of Congress. Any real change was thwarted by RINOs, many in the most conservative of states.
In fact, about the only good thing that occurred in six years of Republican power was the nomination of conservative judges to the Federal courts, something that was only accomplished because the base stood on principle and made it clear RINOs that oppose such judges would not be re-elected.