Elias here with Shopify Support. Thank you for reaching out.
Alternatively, you can also consider using a third-party search app to improve the searchability for your store. Apps, like Product Filter & Search or Smart Product Filter & Search, include features that can help with instant suggestions, spellcheck, and typo-tolerance. If you need any assistance with these apps, you can always reach out to the developers directly through the contact information found in the Support section of their app pages.
Do customers search by SKU often? Does adding other variations of the SKU to the product tags work for you?
You should be able to. Just follow the formatting rules for the spreadsheet here, and add your tag to the comma-separated field in the appropriate column.
If you'd like further assistance, please let me know.