Would applying through my wife who is a US citizen help me get a green card faster even though I'm on deferred action?

As the immigration law stands today, you cannot get a green card. Deferred Action for Childhood Arrivals (DACA) does not entitle you to a green card, only to a 2-year work authorization. If you have it, you also do not have to fear being grabbed and deported (for now, anyway). But DACA does not carry a promise of a green card. Being married to a U.S. citizen also does not entitle you to a green card. If you had entered the U.S. on a visa, legally, and your U.S. citizen wife would successfully petition the U.S. government for an immigrant visa for you, than your unlawful presence could be forgiven, and you could have got a green card. But, without a legal entry, you cannot adjust status - unless ICE starts removal proceedings against you, and you prove to the Immigration Judge that you are in the U.S. for over 10 years, that you are a person of good moral character, and that your deportation would cause an exceptional and extremely unusual hardship to your U.S. citizen (or permanent resident) wife, child, or parent. Since, by giving you DACA, the government promised not to try to deport you, the last scenario is unlikely for the next couple of years. So, the only hope for a green card for you is a change of the law. The talking heads of the national media make it look like that an immigration law reform is about to happen, and that it is going to be a very big, comprehensive reform. We shall see. And it is likely that DACA beneficiaries and spouses of U.S. citizens will receive some form of legalization. Just be patient.

You are not going to be eligible for adjustment of status to permanent residence under the current immigration laws, even though you are married to a US citizen, if you entered the US unlawfully. Deferred action and green card are not the same and whereas you may be eligible for the DACA under the newly passed law, the green card path is still not available to you at this time.

Presently, you cannot get a green card through deferred action or DACA. The only way to get a green card is if you are petitioned by a relative or employer. If your wife is a U.S. citizen, she can petition for you. I suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case, advise you of your options and, if possible, make sure that the necessary paperwork and documentation is presented so as not to delay the process.

A petition filed by your US citizen wife is probably the fastest way for you to obtain full permanent resident status. As you know, DACA or deferred action is only a temporary discretionary fix and is subject to withdrawal in DHS' sole and unreviewable discretion.In fact, its future is uncertain. Therefore, your spouse should immediately file a Form I-130 petition for you. Upon approval, you should file the I601 provisional waiver for unlawful presence. I am reasonably optimistic that your I-601 waiver will be approved since you appear to have satisfied the discretionary factors necessary for DACA. You can then visa process overseas and with assurance, you'd be allowed to return States side as a lawful resident.I have advised several times in this forum of the wisdom of hiring an experienced immigration attorney in almost all matters before DHS and I do so in your case as well.

Yes, your wife should petition for you and after the petition is approved you will need to file a waiver for unlawful entry.

Because you entered without inspection, you may not be able to adjust status based on your wife's I-130.

If your marriage is real, you have appropriate documentation to support your wife's petition, and your wife can support you by an affidavit - that is probably the way to go for you in your situation.