Does using the radio alert enemies to my presence?
As confirmed on the Steam Forums, using the radio does not appear to impact on your ability to sneak.
I have personally noticed what I perceive to be attention to my radio, however, not any more then I noticed in Fallout 3 and New Vegas. Double checking my sources for the purpose of this question, it appears that the radio did not directly effect sneak in Fallout 3 nor New Vegas.
Coomie makes a good point, regarding the fact that using the light definitely does decrease your chances of sneaking. However, keep in mind that the light has a hotkey to turn on and off, where as the radio does not. If radio decreased your chance of sneaking, you would have to manually turn it off before a perceived encounter, and bother to turn it back on again, afterwards. The radio also mostly adds atmosphere to the game, compared to the light, which serves to suit a specific function.