Sure can! As long as the video owner "turned on" that option when they uploaded them. From Microsoft:
Office 365 Video
Download for offline viewing—Stay informed and up to date even when you are not connected to the Internet. Office 365 Video enables the ability to download the file to your local machine or easily transfer to your smaller device for times when you need to view a video offline or to show a video in a location without Internet access. Channel admins can control who is able to download videos based on the same permissions for the channels (owners, editors and viewers).
Once enabled, viewers can take a copy of the video for offline playback by clicking the Download button directly under the player on the player page.
Learn more about how to set download permissions within the channel permissions settings.