Can I file Form 14653 using turbotax? If not, can I just file the three years required by 14653 using turbo tax, then combine it with the paper submission of the form?

TurboTax does not support Form 14653.  However, you can use TurboTax to prepare the returns that you wish to submit under the Streamlined Foreign Offshore procedures.

After you complete the returns, assemble the package for filing manually.

To find the TurboTax products for prior years, please click on this link: TurboTax Prior Year Products.

Disregard the filing instructions that print with your tax returns. Mail your returns and all required forms and documents to the address listed in the instructions for the program. You will find those instructions at this link: Streamlined Foreign Offshore Procedures.

Thank you for your reply. This is very helpful. When I try to finish my taxes on the turbo tax service, so I can send them in by email as you have recommended, I get flagged during the check process.

The issue that is being pointed out here is that "all of the following lines from Form 1040 have a zero value".

Should I just ignore this and proceed to file?

You should de-select the e-File option and choose "File by Mail".  Ignore the errors related to the zeros, print the returns, and mail them into the address that is specified on instructions page for the program (link below.)

Please visit the instructions at this link Specific instructions for Streamlined Foreign Offshore Filing. and Follow them very carefully!!!  

Keep in mind that while you can use TurboTax to prepare your tax returns, we do not support the form or that program.