English grammar was heading in the less-inflected direction before the various creole-hypothesis invaders started making their mark on the language.

For the Middle English creole hypothesis, yes--OE was losing its inflections in the Danelaw as a result of contact with Old Norse, which had a lot of substantially similar core vocab and the same word order but different inflectional endings. But there's also the argument for creolization with a Celtic substrate to account for things like the progressive tense and do-support, which don't occur elsewhere in the Germanic family but are common in Brythonic.