Once my OIC is accepted, does interest still accrue?

Yes.  Once your Offer in Compromise (OIC) is accepted, interest accrues but the taxpayer's requirement to pay it is suspended.

What is an Offer in Compromise (OIC)

An offer in compromise (OIC) is an agreement between the Internal Revenue Service (IRS) and the taxpayer in which the IRS agrees to settle the taxpayer's past due tax liability by accepting an amount that is lower than the total past due amount. For example, if Mary owes $1000 in back taxes, she can ask the IRS to settle for $800. Once the IRS accepts an OIC, interest continues to accrue on the past due amount, but the taxpayer's obligation to pay the interest is suspended until the amount agreed to in the OIC is paid off in full. If the taxpayer fails to pay the OIC amount in full or defaults on payments, the IRS will then add the accrued interest to the full past due amount. Assume Mary's OIC to settle her $1000 past due tax liability for $800 is accepted by the IRS and she requests a payment plan of $100 a month to pay off the settlement amount of $800. The IRS will continue to calculate interest on the total amount due, but Mary will not be required to pay that if she continues to make her monthly payments and pays the amount in full.

Consequences of Default on an Offer in Compromise

However, in the earlier example, if Mary were to default on her payments, the entire past due amount would become due plus the accrued interest. Thus is it in her best interest to think carefully about her financial obligations and abilities before agreeing to an Offer in Compromise with the IRS. That money and more (due to the continuously accruing interest on the principal) will always remain due to the government. Thus there is no true default mechanism for Offers in Compromise.