The answer to your question depends on what boxes you checked on the 4506-T form that grants lenders access to your tax documents.
If you checked box 6A then lenders have access to your return transcript which includes most of the information contained in your tax return(s) filed with the IRS. Please note that a tax return transcript only shows information based on the tax return as filed and does not reflect any amendments or updates to your tax return after it was filed.
The lender uses the information in the return transcript to verify the information contained in the tax returns you provided when you submitted your mortgage application. You are usually required to provide your tax returns for the prior two years when you apply for a mortgage.
If you checked box 6B on the 4506-T form then lenders have access to your account transcript which includes information on payments, penalties, assessments and adjustments made to your account after you filed your taxes. Any outstanding tax liens or current payments you make for back taxes should appear on your account transcript.
If you checked box 6C then lenders have access to a record of account which is basically a combination of the return transcript and account transcript so it provides comprehensive information about your tax account and returns.
Please note that the tax documents outlined above are usually available for the current tax year and the previous three years. Additionally, the 4506-T form only applies to your federal tax returns and account and does not provide the lender access to information on your state or local tax returns. Generally, lenders only review your tax transcripts for the prior two years
Returning to your question, if you checked box 6B or 6C on the 4506-T form then the lender gains access to your tax account transcripts and may become aware of the back taxes you owe and any ongoing payments. If you only checked box 6A, then the lender does not have access to your account transcript and may not learn about your back taxes or any outstanding tax lien. In most cases, lenders only require applicants to check box 6A.
We should highlight that if you are paying back taxes according to a plan agreed to by the IRS, the monthly payments should be included as debt in your debt-to-income ratio, which may reduce the mortgage you qualify for. Depending on the amount of your tax payments, you may need to reduce your loan amount or lower your other monthly debt expenses, if possible.
The good news, however, is that you do not need to pay off the full amount of the taxes you owe as long as you provide a copy of the agreement to the lender, you are current on your payment plan and the IRS has not filed a tax lien against you in the county in which the property being financed is located. If you do not meet these requirements you may need to pay off your back taxes in full to qualify for the mortgage.
Form 4506-T: https://www.irs.gov/pub/irs-pdf/f4506t.pdf
Mortgage Guidelines for Federal Tax Payments: https://www.fanniemae.com/content/guide/selling/b3/6/05.html#Federal.20Income.20Tax.20Installment.20Agreements