No, the IRS won't forward a refund check. Instead it will be returned to the IRS. If you don't think you will receive it in time, you could try to contact the IRS and state tax authority to see if they can help you before your refund is processed.
Also, you can submit a Form 8822 to change your address with the IRS. They may not receive it until the refund is processed, but the new address will on file with them. Go to this link for that form https://www.irs.gov/help-resources/tools-faqs/faqs-for-individuals/frequently-asked-tax-questions-an...
IRS Telephone Assistance for Individuals:
Toll-Free, 1-800-829-1040 Expect long wait times.
Alternatively, this link has the local IRS offices. After going to the link, you can scroll down the page then click on the map for your location. https://www.irs.gov/help-resources/contact-your-local-irs-office