Oh why not? As the other commenters above have already pointed out, gay couples probably go through the same issues as us! We are all humans after all. I would imagine that gay partners might have issues about personality dominance, especially since the spouses are of the same genders. However, sometimes being part of a gay couple can be wonderful because your partner is of the same gender and can probably understand what you're going through!
I think all couples will experience the same ups and downs regardless of their sexual orientation. The context might be different, but everyone has the same social and psychological basic needs that they hope can be met but does not come as easy as they thought. Gay couples who are looking to go for counselling should seek a professional who specialises in LGBT relationships as they tend to understand the relationship dynamics more.
Gay couples typically experience the same or similar issues as their heterosexual counterparts, and can benefit from counseling in comparable ways. Every romantic relationship experiences conflict, and the way we learn to resolve conflict is based on what our parents have modeled for us. In most cases, the tools we’ve learned this way are riddled with problems and don’t always work for us the way they did for our parents. When you exhaust your known strategies for coping with relationship problems, that’s when it’s a good time to start looking for a couples counselor, who can help by giving you new tools.