Hello Liew,
Thanks for submitting a question on importing .ai Adobe Illustrator files into a BoldGrid site. You can certainly import and host files in virtually any format on your web server, and you make them available for download if you desire.
But if you mean importing for the purpose of displaying the image on your site, you can, but you will first need to export the image it to a web safe format like .jpg, .png, .gif, etc. Illustrator has templates you can use to produce high quality images for the web. I advise checking the support documentation for your Adobe products to learn more about the various formats they support.
WordPress (and thus BoldGrid as well) support all the formats that are supported by the web browser. These will vary, but the most popular browsers like Firefox, Chrome, and Safari will support the formats mentioned above. It is always wise to use a format that is widely tested to work well across all browsers to ensure a satisfying experience for multiple users.
Best,
Christopher M.