Well, if you genuinely want a braindead alternative to `vim-conda`, you're welcome to this brittle hack I use. (For my purposes, fast-and-dirty has been an efficient solution, but I don't actually recommend this to anyone.)
Add it to your `ftplugin/python.vim`. Requires you to have activated the Conda environment before opening the Python file, uses hard-coded Python versions, doesn't work with multiple environments, doesn't bother with `os.path.join` so no Windows compatibility, etc etc. Like I said: a hack.
" Cheap trick to use the Conda environment with omnicompletion
python3 << EOF
import os
import sys
cenv = os.environ.get('CONDA_PREFIX')
if cenv is not None:
# Taken from `sys.path` as reported by ipython
sys.path.insert(0, cenv + '/lib/python3.5/site-packages')
sys.path.insert(0, cenv + '/lib/python3.5/lib-dynload')
sys.path.insert(0, cenv + '/lib/python3.5/plat-linux')
sys.path.insert(0, cenv + '/lib/python3.5')
sys.path.insert(0, cenv + '/lib/python35.zip')
sys.path.insert(0, cenv + '/bin')
EOF
set omnifunc=python3complete#Complete
edit: mentioned `os.path.join` to warn Windows users and fixed in-place bugfix.