No. The WSJ prime rate is 4.25%, even the Fed prime rate is 1.75%, way above the 1.20% you'll be making from your savings account. If you are high worth individual with great credit history, the bank might give you a personal loan at 4.25%. They won't care what you do with it as long as they get their payments.
If you are not that creditworthy, they'll ask for a collateral, you can mortgage your house for example. It ends up being the sames thing, you get your money and do what you want with it.
If you can make more than the interest rate the bank gave you, great, you made profit. The bank however won't agree to lend you money at 0.6% (1/2 of the 1.2% APY your savings account will bring). Why would they when they can loan that at prime rate of 4.25%??
The closest you can get to something like this is if you are a hot-shot wall street money manager with track record of making big profits. In that case the bank might put some money in your fund for you to manage, but that's not something a regular person can do.
Your plan as proposed will not work, because it goes against how banks make money. Banks make money in two ways:
(1) Fees [including account fees, investment advice fees, mortgage application fees, etc.]; and
(2) Interest Rate Spread. They borrow money for x%, and they lend it out for x+y%. In a simple form, someone gives the bank a deposit, and earns 1%. The bank turns around to the next person in line and loans the money to them for 4%. You are asking them to turn the interest rate spread into a cost instead of their main source of profit:
You are asking the bank to borrow money from another person paying them 1.2% interest, and then loan the money to you, paying you 0.6% interest and keeping 0.6% for themselves. The bank would lose money doing this.
Technically yes, you can borrow from a bank and invest it in something earning above the 4% interest they will charge you. You can then pay the bank's interest off of your earnings, and make some profit for yourself. BUT this carries an inherent risk: If your investment loses money, you still owe the bank, effectively increasing the negative impact of your investment. This tactic is called "Leveraging"; you can look it up on this site or on google. It is not something you should do if you do not fully understand the risks you are taking on.
Given that you are asking this question, I would suggest tactfully that you are not yet well informed enough to make this sort of investment. You run serious risk of losing everything if you over-leverage (assuming the banks will even lend you money in the first place).
There are many flaws with your idea.
Say I want to borrow $225,000.00 to accrue interest on a 1.20% APY account. I promise ... that I cannot withdraw nor touch the account by legal contract.
If you break the contract and lose the money, the lender is out the money. They can take you to court and will win, but if you don't have the money, then they don't get paid. (You can't squeeze water out of a rock even if a judge orders you to.)
By sharing the interest with me on a loan, they keep a percentage that they'd normally get...
If you're "investing" the money at 1.2%, and the lender gets some amount less than that, then they are getting much less than they "normally" get. Lenders typically get somewhere from 5-15% on loans.
The money can also be used to fund a stock/trading account. Regardless of whether I profit, I pay interest on the loan and split the profit shares 24/7. How can the lender lose with legal enforcing?
Again, if you lose the money, no amount of legal enforcing can force you to pay money that you don't have. Even if you go to jail for fraud the lender still doesn't get paid.
Simply, no bank would ever agree to this.