The Lenovo T470P is almost completely supported by Linux. Exception is the fingerprint reader, is not supported. The T470p different from the T470 with a modified CPU configuration and the lack of a USB-C / Thunderbolt port. An overview can be found here:

https://wiki.archlinux.org/index.php/Lenovo_ThinkPad_T470

I use the device with a Lenovo Docking Station, which out-of-the-box works well. Compared to my previously used W530 a dream, because there the docking could be operated with an external monitor only means bumblebee because of the built-in Nvidia graphics. Solely the sound could not be output via jack but only via DisplayPort. researched briefly turned out, that the problem has already been reported as a bug:

https://bugzilla.kernel.org/show_bug.cgi?id=195161

With the release of Kernel 4.15.5 the problem was partially solved. However, there are currently some problems, if the unit from standby to start. The sound will no longer function, but will certainly be addressed in a next kernel update.