Apart from the fact that I am a die-hard C/A shipper, I think Groo wasn't the right person for Cordelia:
Groo would have perfectly well fit with the old Cordelia ... a boyfriend that was devoted to her, even worshipped her, thought her flawless, acknowledge her for her beauty and could even see the warmth in her heart. But that would not be enough for the new Cordelia, the one that found her purpose in life, was very well capable of taking care of herself and needed to be challenged.
When she came back from her vacation it was obvious that there already were slightly annoyed by his overprotecting and naive behaviour. Groo would have needed to change a lot in order to keep Cordelia happy. She confessed to Angel that part of her motivation to become involved with Groo was that she felt tired of being alone. She knew the chances to actually meet someone who can stand the life she was living were very slim and she took it when it was presented to her.
But all in all I found Groo was kind of a surrogate Angel for her, a champion, who she did admire for his strength, his courage, his kindness and the goodness in his heart, all traits she praises in Angel as well. But since she never allowed herself to see Angel in a sexual way because of his curse, she re-directed her feelings towards Groo. But though he was sweet in a very naive, child-like kind of way he never came near to understand her like Angel did, who provided her with her purpose in life and cared for her without actually diminishing her abilities.