There is no way of knowing who or how many of these Trump supporters exist and they will continue to have influence up until the election. It is important not to discount these people and the effect they will have when predicting the results of the election in November and beyond.
This is one of the worst election years in history. I can only hope the "secret" Trump supporters have finally reached a point where they are disgusted enough with his racism, bullying and general idiocy and won't vote for him. As it stands now, a vote for any third party candidate seems to me to be a vote for him. I imagine some of the old-school conservative "party of Lincoln" Reps can't in good conscience vote Trump. I have no clue about the secret supporters.
Secret Trump supporters will influence the election because they will impact the number of electoral college votes Trump receives. Secret Trump supporters may have even more influence; if they feel they must be secretive, they probably live in an area with more liberal voters. If there are enough people who secretly support Trump, their votes could be important because they could help win over areas that are predicted to vote for Clinton.
No, the supposed "secret Trump supporters" will not influence the election because they do not exist. Trump has claimed that he is backed by the "silent majority": people who agree with his views but who have been too oppressed by liberal political correctness to say them out loud. This is a method of excusing his more racist, xenophobic, and otherwise offensive views; by claiming that he is just saying what everyone else is thinking, he paints himself as a brave outsider and voice of the people rather than a demagogue who divides people. While this might be a decent rhetorical strategy, it doesn't translate into actual votes for Trump. At this point, foreign policy Republicans, Ted Cruz, and other prominent GOP politicians have abandoned Trump and some support Clinton. Even assuming they existed, any "secret" supporters have to be balanced by the traditional Republican base that Trump has alienated.