The short answers are Yes and No, at least with the HV40. You can stream without recording video with correct output, and when/if you do start recording it will not "kill" the stream. The HV40 has HDMI outputs, 1394 outputs, component as well as A/V. You can use the 1394 output without issue and be able to record at any time. The only hitch is that if you have TC or date/time turned on/display, you will see this in your stream as well as anyone else who is watching your stream. You may also see your tape length and or tape info.
To recap: just make sure you do not have those functions/display turned on and you should be fine. I have used my HV40 streaming and have not had any issues at all.
Hope this helps a little.