From my perspective anarchist ideas are what truly undermines the colony. The colony has always been a specific form of organization originating out of mechanical philosophers such as Descartes and Hobbes who used the mechanical metaphor (the heart as a machine, the social body as machine) as the outline and construction of the state. Put simply, the state form of organization is the colony, embodying a complicated set of relationships and reason for existence, justified by words like "progress," "modernization," and "development." This is roughly how I approach this question and ask, "What is decolonization?" Implying, how do we break the colony, its racism, sexism, and generalized inclusion into a system or regimented order--how do we create our own relationships and maintain autonomy, and live a dignified and content life? Not to forget, how do we deal with a system that coerces us, humiliated us, and in many ways just socialized us to a way of life that was not of our choosing, or better imposed choices--providing a menu or framework of choice and life.
For me, the only political theory that has the potential to realize decolonization is anarchy and maybe anarchism. This is the challenging of state structures--this is challenging at its core the colonial structure, which is no longer corrupted, but rotten to the core in its very function and socialization, arguably treating Human, non-human people, and the natural environment as natural resources to build the wealth of the colony (aka state). Decolonization to me puts into question the role and function of the state, notions of progress, and specialized order it necessitates. For me anarchy and (some conceptions of) anarchism constantly try to undermine the state and colony making new spaces for experimenting with decolonization and how to reclaim our social relationships, break down social barriers between people, and begin to address the systemic problems and tensions that prevent projects and experiments with decolonization.
So yes, I believe ideas of anarchy have great insights into decolonization, but again I think of decolonization as a response to the colony organization and what it breeds. To really decolonize we need to challenge the colony organization and realize that colonialism and internal colonialism are just two sides of the same coin of capitalism that play the home and the periphery against each other--with greatly different and varying forms of intensities of violence and "soft" or friendly controls, but at the end of the day our lives are offered to the order of the colony and its conception of progress.
You ask, "If it can, what are those insights?" It is hard to answer, it all depends how far you want to take decolonization and acknowledge the deep-seated effects of living within the state/colony. People have always been trying to figure this out with many experiments, projects, and so on. But for me, I don't want a new party, mode of industrialization, and forms of social control--police formal and informal. I would like to challenge the colony and try to experiment with opening up spaces of contention and attack that are difficult to recuperate and re-brand that often end up extending and intensifying state control and its economy. For me this is a deep and long life question where there is no easy answer, but for me this is a question first and foremost: how far do you want to take decolonization in your life--do you want state integration or decolonization of the very relationship and structure imposed by the machine? These question might help to determine how you want to struggle within the colonies of the world--"democratic" and authoritarian.
I guess the question is for me is this: we are all fucked up, confused, hurt, and some with more than others, but how are we going to deal with the colony and its effect on our lives for fulfillment, dignity, and for fun.
Hope this is useful in some way.