Can I use Quicken 2017 in High Sierra?

Yes.

Quicken 2017 runs perfectly fine in High Sierra.

I don't have it, so I can't say for certain, but Intuit's site isn't clear, either. For both Quicken 2017 and 2018, it just says Sierra or newer. "Newer" would have to be High Sierra, but still, it doesn't clarify that it works.

Contact Intuit. They would know.

Mac

2018 Release

• Computer: Intel Based Macintosh
• Operating Systems: Mac OS X 10.11 (El Capitan), 10.12 (Sierra), or newer
• Memory: 256 MB or greater
• Hard Disk Space: 100 MB
• More memory and hard drive space may be required for large data files
• Display: 1280x800, 1366x768 or greater
• Internet Connection: Broadband
• Quicken ID: Online access is required for registration.

Quicken for Mac 2017

• Computer: Intel Based Macintosh
• Operating Systems: Mac OS X 10.10 (Yosemite), 10.11 (El Capitan), 10.12 (Sierra), or newer
• Memory: 256 MB or greater
• Hard Disk Space: 100 MB
• More memory and hard drive space may be required for large data files
• Display: 1280x800, 1366x768 or greater
• Internet Connection: Broadband
• Quicken ID: Online access is required for registration.