The Anglo-Saxons lived in England before the Vikings arrived. So no, they are two distinct languages. The Angles and the Saxons came from Northern Germany, long before the Vikings decided to invade. The Viking invasion was significant, heavily influencing English society and language. Many old towns in England still have the old Norse town ending -by.
Effectively, there are three main sources for English:
* The Anglo-Saxons, arriving around the time where the Romans left.
* The Vikings, arriving around 800-1000.
* The Normans, arriving around 1066.
Not that English haven't changed significantly since then, but these three periods represent the largest number of words increases. The other changes have primarily been spelling.