I ended up writing this snippet that uploads webpack assets to the static storage. This might be useful for someone else and couple be included in webpack-loader itself.
from django.conf import settings
from django.contrib.staticfiles.storage import staticfiles_storage
from webpack_loader.utils import get_loader
for config_name in settings.WEBPACK_LOADER:
    loader = get_loader(config_name=config_name)
    chunks = loader.get_assets()['chunks']
    for assets in chunks.values():
        for asset in assets:
            with open(asset['path'], mode='rb') as f:
                staticfiles_storage.save(asset['name'], f)