Probably not - most plans only allow in-service employees to utilize loans. Once you separate from service the loan needs to be paid back or else it will be considered a distribution. You typically have 60 days to repay the loan before a deemed distribution will occur, but I suggest checking with your 401(k) administrator.
Here is some more information: What is a 401(k) early withdrawal?
Whether you can continue to pay the 401(k) over time is governed by the terms of the 401(k) plan. You'll have to ask the plan administrator. As MindyB indicates, in most cases the plan requires an offset distribution (not a deemed distribution) to be made, effectively paying off the loan using funds in your 401(k) to satisfy the loan and treating it as a distribution.
Thanks for your response. I read this, "The 2018 Tax Reform law extended the repayment period for your 401(k) loan until the due date of your tax return, including extensions." Is this still in effect?
Yes, if you receive an offset distribution and the Form 1099-R that reports this distribution includes code M in box 7, you have until the due date of the tax return for the year in which the offset distribution occurs to come up with the funds to complete a rollover of some or all of the offset distribution.