No, conda update and conda install don't update packages installed with pip (or install them using pip).
These conda commands only check your "default" anaconda-channels or the ones specified with -c, they ignore everything else. One exception is conda list which shows also the packages installed with pip, these are marked with <pip> and won't be updated.
One example using pip and six:
$ conda create -n testenv python=3.5
Fetching package metadata .................
Solving package specifications: .
Package plan for installation in environment testenv:
The following NEW packages will be INSTALLED:
pip: 9.0.1-py35_1
python: 3.5.3-3
setuptools: 27.2.0-py35_1
vs2015_runtime: 14.0.25123-0
wheel: 0.29.0-py35_0
Proceed ([y]/n)? y
$ activate testenv
Installing six with pip (old version):
(testenv) $ pip install six==1.6
Collecting six==1.6
Downloading six-1.6.0-py2.py3-none-any.whl
Installing collected packages: six
Successfully installed six-1.6.0
conda update doesn't update it (note that six isn't listed in the "all requested packages" but it's listed in conda list):
(testenv) $ conda update --all
Fetching package metadata .................
Solving package specifications: .
# All requested packages already installed.
# packages in environment at testenv:
#
pip 9.0.1 py35_1
python 3.5.3 3
setuptools 27.2.0 py35_1
vs2015_runtime 14.0.25123 0
wheel 0.29.0 py35_0
(testenv) $ conda list
# packages in environment at testenv:
#
pip 9.0.1 py35_1
python 3.5.3 3
setuptools 27.2.0 py35_1
six 1.6.0 <pip>
vs2015_runtime 14.0.25123 0
wheel 0.29.0 py35_0
But it can be upgraded with pip:
(testenv) $ pip install six --upgrade
Collecting six
Using cached six-1.10.0-py2.py3-none-any.whl
Installing collected packages: six
Found existing installation: six 1.6.0
Uninstalling six-1.6.0:
Successfully uninstalled six-1.6.0
Successfully installed six-1.10.0
Just to show that there is a newer version of six in the anaconda channel (which was ignored when I did conda update):
(testenv) $ conda install six
Fetching package metadata .................
Solving package specifications: .
Package plan for installation in environment testenv:
The following NEW packages will be INSTALLED:
six: 1.10.0-py35_0
Proceed ([y]/n)?