The short answer is no. C/F cabin passengers don't get any privilege at TPE.

The best you may consider is "expedited check-in and immigration clearance" via Huan-Yu VIP Terminal (環宇商務中心), which is a paid VIP service. I have a more detailed post about TPE speedy and/or VIP services in another old thread:

https://www.flyertalk.com/forum/22883317-post3.html

ps. Some hyperlinks to the governments might not be valid due to websites makeover/s since 2014. However, the process still remains the same.

As for in city check in, I haven't had a chance to use it. It should save you time. Having said that, I did have the pleasure to see the news coverage on the temporary service interruption/suspension of airport MRT and/or in-city check-in several occasions for hours due to software glitches/electrical malfunction/weather in 2019. IIRC, the interruption happens more often this year than prior years. I just don't know why. I don't mean to scare you. Just make sure you have a backup plan when things go south.

Hope this helps.