True. Although that distance will of course increase with time. Can't predict how weak our signals would have to get before they couldn't be distinguished from background noise, though.....
The key to "communication" with aliens, either with us detecting them or vice versa is less about the content of the message and more about looking for artificial radio transmissions, which, if you know what to look for, stand out like a sore thumb. A broadcast of Happy Days
'looks' very different to background radio noise, even if the actual content has degraded beyond retrievability (and, in the case of Happy Days
, probably for the best if we want the aliens to bother replying
) the repeating, ordered nature of the signal may still send up red flags with a passing alien.