No, until the divorce is finalized you will need your "soon to be ex " to sign a quite claim deed, and allow the lender to run a credit report, the debts on the credit report may be counted against you.
If you can not qualify with those debts and or if she will not sign, you should probably cancel the escrow quickly. Make sure you state in your reason for withdrawing one of the contingencies that written into the contract so that they have to give you back your deposit. So you would not say I am withdrawing because of a divorce but rather the inability to obtain a mortgage.
Remember the contingencies have time periods, if you wait too long and cancel after the contingency period, the seller has legal justification to keep your deposit and maybe even sue you for damages.
When buying a house you need a lender who understands the homebuying process. Few do.