Once you get the misc topic, investigate DG, if you dont initiate it, will the random attacks happen anyway?
Random attacks on towns might never happen unless you start the questline, depends on what your character has done, you can continue to ignore it and just continue what you are doing, but once you have heard of the attacks you should make some preparations to protect NPC's just in case, and keep an eye out for unwanted visitors.
Attacks are never going to happen straight after escaping from Helgen, not unless you go join the Dawnguard before you get the hints, or you discover some very rare glitch.