If I am not part of a lawsuit to contest a will, can I still benefit if they are successful and I am a rightful heir?

I think you answered your own question: You are not willing to pay-to-play. That means you are willing to accept things the way they are. If the present scheme does not include you, then you can't do worse than that if the contestants prevail. Who knows, you might even get a windfall.

If he didn't have a previous will, than you would be correct.

If the matter went to trial and there was a judgment that the Will was invalid, then the Will would be totally invalid as to everyone. There either is a valid Will or there is not one. You do not have to be part of the lawsuit to benefit from its results. The probate judge would probably have the power to award recovery of their costs [which may or may not include attorney fees] to the litigating parties as they have caused a common fund for the benefit of all heirs. Even if the successful contesting of the Will did not apply to the non-litigating heirs, they could use the judgment as res judicature against the losing party. The problem you may have is the suit will probably be settled before any judgment or verdict issues, and the successful litigating heirs may not be willing to include you unless you pick up a pro rate share of all their costs, including attorney fees. But that would put you in no worse a situation then if you hired an attorney who took an active role in the suit [if your attorney merely files suit and lets the other attorneys do all the work, then his/her fees should be substantially less. You have to make a guess as to how likely it is that the possible scampers will be willing to settle for a substantial amount.

If there is no will, then direct descendants down two layers if there are grandchildren whose parent has died before the grandparent estate is probated. If there is a will, then to the persons named in the will inherit. Only the alleged executor/administrator can bring a lawsuit on behalf of the estate; others outside who want to sue, must file for authority from the court to sue, and the executor/administrator can join or reject the suit. You are advised to seek the counsel of a probate litigation attorney to represent you regarding your beneficial interest in the estate. This is called beneficiary representation, and the attorney may take the matter on an hourly rate or a percentage of your alleged share of the estate in representation of you. Do not agree to pay costs with the cousins unless you have had good legal advice, and be prepared to pay for the advice.

There's another reason why you might not wish to participate. If the will was drawn by a lawyer it probably has an anti-contest clause, which says that if anyone contests they get nothing. Of course if the contest is successful the will gets thrown out anyway, so the clause is meaningless. You are correct. If the will is found to be the result of undue influence, the entire will would probably be found to be invalid. The estate would then go to the decedent's heirs. Without more facts, however, it should be said the the court could find a partial invalidity.