No. My wife and I both consider ourselves anarchists. We've been together for over two decades, and have come to the idea of anarchy as a couple over the years together. Although we both feel deep down we've always rejected hierarchy and domination, now it's a more conscious choice that we seek to live more fully, and walking together in conflict with the dominant narrative in society gives us strength and allows us to explore more ways we can live and think differently than we likely would alone. Our relationship seems more free of control, coercion, and judgment than any other I've been involved in, past or present. If I couldn't have that in my most personal relationship, I don't know how I'd expect to find it elsewhere.
I like this question because my impression is there aren't many monogamous couples who are anarchists, and I was wondering the same thing myself.
A couple of years ago we were looking for intentional communities and ended up contacting one that was polyamorous (it wasn't entirely obvious from the outset), and they weren't interested in us visiting because they thought we'd always side with one another over the concerns/needs of the group, despite the fact they apparently used consensus decision making. Anyway, we had no problems with the fact it was polyamorous and wanted to at least check it out, but to no avail. The folks I dealt with via email were very friendly and thoughtful, however.
I think the view many people have (that poly group for example, and perhaps some anarchists and non-anarchists alike) is that marriage or monogamy automatically constitutes some form of control, or co-dependence, or lack of freedom. For us personally, our relationship has expanded our sense of self, of freedom, our ability to live creatively, and it's a living work in progress of mutual aid and acceptance without hierarchy. It seems a natural desire to me to extend that type of relationship with other people besides each other - the difference being our level of intimacy in certain ways (some obvious, others not so), but that doesn't mean we don't have or want high levels of mutual aid and intimacy with others in varying ways and to varying degrees. To the contrary, it feeds our desire to find more of it.
EDITED: to change the short answer from "yes" to "no"! I was thinking the question was phrased in the affirmative. If my answer were yes, it would invalidate me. :)