No, Heidegger explicitly attempts to refute and attack Descartes's supposition "cogito ergo sum" (the first therefore). And one can read all of Heidegger's early philosophy as an attempt to undo the errors started by Descartes: Heidegger faults Descartes with stymieing all of modern philosophy with a false first presupposition.

Heidegger's fault with Descartes lies in the very first two words: "I think." Heidegger does not believe that the "I" (Dasein/Being) is the thing that thinks (directly at least). In Descartes' world, humans are "res cogitans" ("thinking machines"): the "I" is that which thinks. For Descartes, there is some thing that is doing the thinking. In Heidegger's world, there is not some mysterious being that thinks, but rather the "I" is the experiencing/thinking itself (the "thrown-openness"). This is why Heidegger always uses verbs/gerunds to describe Being.

For Heidegger, the simple statement "I think" cannot possibly be true because there is no "I" behind the thinking. For Heidegger, the analog basic first-claim would instead simply be: "there is thinking" (the "ego"/"I" as we think about it is the "thinking" itself for Heidegger).