Yes, you can listen to all Radio One stations at https://www.cbc.ca/lite/radio/live-radio. Select a station to load the radio player.
The CBC Lite radio player is set to remain at the lowest available bitrate setting for the chosen station, meaning quality may be slightly decreased in order to save on data consumption and increase stream stability.
You can also view episode transcripts of both The Current and As It Happens from their respective landing pages. Within episode stories find the “Episode Transcript” link to view their transcripts.