No. Trust me, I have just been through this.
All of your money in BCT is deposited into a special military bank account on the 1st and 15th of every month you are there, and then the remainder at the end. You don't need money in boot camp, everything is either issued to you or deducted from your pay.
Your wife will be on her own, sorry.
However, AFTER BCT, you can have whatever account you want. Military paychecks are all direct deposit, and they can do it into whatever accout you want them to. I HIGHLY recommend Well's Fargo military account (it can be a joint account). The difference with this account vs. other accounts is free online bill-pay, free checks, and you can withdraw money from any ATM in the WORLD without a service charge.
But for boot camp, it has to be a special account, and you aren't allowed to send money home, and your wife is not allowed to withdraw money from that account.
You will leave BCT with a lump sum of about $4,000.
I went through this and I had to actually get a temporary job while my husband was in BCT since I didn't previously have a job and we still had rent and bills to pay and food to buy. So I worked for the 3 months he was in training until he begain receiving regular paychecks..
Also, you don't receive BAH in BCT either. All of the military benefits kick in after you graduate because you aren't considered a "marine" while in boot camp.