The text does support this idea. First of all, Beowulf is an epic poem and Beowulf is an epic hero in the tradition of the genre. He is strong and courageous, fighting for the benefit of others; however, he is also motivated by pride--the desire to achieve greatness, to bring glory to his people, and to have his name endure throughout history. In an epic hero, pride is not a negative trait; it is one of his essential characteristics. The intent of the epic poem itself is to tell the exploits of the hero, like Beowulf, and keep his name alive among his people.
Beowulf leaves his home and crosses the sea to battle Grendel not only to save Hrothgar's people, but to achieve glory. His words to Hrothgar are revealing:
I have come so far . . . that this one favor you should not refuse me--that I, alone and with the help of my men, may purge all evil from this hall. I have heard, too, that the monster's scorn of men is so great that he needs no weapons and fears none. Nor will I . . . my hands alone shall fight for me, struggle for life against the monster.
To achieve the greatest glory, Beowulf seeks the greatest danger--to fight Grendel with his bare hands.
Grendel's role in the poem is deeply symbolic. He is the personification of evil itself, a monster born of monsters who had been born of Cain and banished by God to be punished forever. Grendel is a"sin-stained demon." In his characterization, pride becomes a sin, an expression of selfish will. Grendel destroys for the love of destruction, to exercise his will over the Danes. Just as Cain's killing Abel was an act of selfish will, Grendel's actions are those of sinful pride. He takes delight in being vicious, preying upon the sleeping Danes in Herot.
Grendel and Beowulf both can be interpreted as acting out of pride, but certainly not in the same way. Beowulf takes pride in his strength and courage, choosing to defend goodness against evil. Grendel takes pride in bringing darkness to Herot, once a place of light, fellowship, and security.