according to this manual (and the manual of TriPure) everything looks great.
In reality though, most people that have tried that (me included) always prefer to do a separate extraction for proteins only for a number of reasons - isolating protein from the phenol fraction takes a lot of time and plenty of washes, then you spend time to dissolve the pellet, and finally it is not rare yo find your total lysate as a smear when doing a Western.
If you can afford it go for a TriPrep from MachereyNagel for simultaneous extraction of RNA, DNA and protein (or a similar product from other company) I routinely use for small samples (100 000-200 000 cells) and it works great.
It seems expensive, but it is actually cheaper and more important for us the graduate students- it saves plenty of time :)
Yes it is not impossible! You will find a proteins interphase layerwhen performing the phenol:chloroform:isoamyl alcohol (CIP) RNA/DNA isolation. But this is time consuming and requires a lot of washing steps to get proteins of good quality.