No, they wouldn't. You are not being denied your right to vote, and you are not being denied your right to vote for the candidate of your choice. And the injury you propose is not specific to you nor different from the generalized injury that might apply to the population in general.
It is an open question WHO might have standing or at what point. Most opinions I have seen is that it would have to be another candidate, and that it probably would have to be after they lost. Otherwise the injury is only speculative, so even if they have standing, the court might not consider the issue to be "ripe". Even if the injury might be real for them, if they don't lose, they don't actually suffer the injury.
Most people don't understand how hard it can actually be to get a case in front of a federal court, especially if the case is political in nature.
So why didn't Cruz get that process in motion when he became interested in running for President? Why couldn't he start now, when Trump announced his run, and get it settled in the next four years? I can't imagine Mr. Trump wanting to be President for longer that that.
What is Cruz's hurry? If he got it settled over the next four years, he'd become President of country turning around to a better direction, and with a lot of the DC garbage cleaned out.