The Lenovo T470P is almost completely supported by Linux. The fingerprint reader is an exception, that is not supported. The T470p differs from the T470 in a changed CPU configuration and the lack of a USB-C / Thunderbolt connection. There is an overview here:

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

I am using the device with a Lenovo Docking Station, which works out-of-the-box well. Compared to my previously used W530 a dream, because there the docking with an external monitor could only be operated using bumblebee due to the built-in Nvidia graphics. Only the sound could not be output via jack but only via Displayport. A short research 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 fixed. But there are still problems at the moment, when the device starts from standby. The sound then stops working, will certainly be fixed in a next kernel update.