I wrote a little bit about it
here.
It is important, because the more power supplied, then the higher your SNR(m) will be, thus a higher sync speed. Our routers have the ability to up the power slightly if its struggling after say bitswap or errors. On adsl2+ its not uncommon to see 18dB upon sync but after time it may ramp up to 20dB.
However..... it should be bourne in mind that PSD masks play a huge part in this process too and will cut back power on shorter lines. The PSD masks are much an undisclosed feature.. all I know is there are supposed to be 5 different profiles depending upon line length (for adsl/adsl2+), but I dont know any actual parameters or what tones are masked. At one time I searched to find out more information but drew complete blanks on this subject.
When it comes to VDSL the PSD masks are different again.. and further complicated by multiple sub-channels, each having what appear to be their own parameters.