No, for the two reasons already pointed out: if you're wanting to predict the turn of the seasons from the celestial bodies you do that by observing the movements of the sun, not the moon (the movements of the moon having no connection at all to the turn of the seasons) and if you're observing the movements of the moon for some other reason you wouldn't expect to find the number twelve featuring anywhere in your calculations - the lunar cycle is 29 days and there are 13 of them in a solar year.
The other point to bear in mind is that things used to mark or observe the movements of the celestial bodies are usually fixed - no culture has ever developed a portable sundial, for obvious reasons. A pendant of this kind might well have a religious significance but, if that religion involved the moon or the sun we'd expect that to be signified by, well, an image of the moon or the sun, rather than by anything referring to the movements of the moon.
Archeological evidence from the Star Carr site suggests that the people who inhabited it were most likely hunter-gatherers. They didn't have any domesticated animals, and there's nothing to suggest that they practised agriculture. Hunter-gatherer cultures tend to be seasonal migrants, moving between highlands, lowlands and coast according to where food will be most abundant at any time of year. Obviously for such cultures it's important to observe the transition of the seasons, but the easy way to do this is the way we use ourselves - observing the budding of plants or falling of leaves, the migration of species, etc, etc. And not only are these observations much easier to make than calculations based on the phases of the moon, but they are directly related to the reason why you want to note the progression of the seasons in the first place, which is the availablity of food sources. So observing the phases of the moon in order to identify the season would not be not only a great deal of unnecessary trouble, but also a much less efficient way of making decisions about hunting and gathering.
As for what their religious beliefs were, and whether they involved the moon or any celestial body, there is no evidence at all from Star Carr, and virtually none from any mesolothic site anywhere in the world. Hunter-gatherer cultures that we have observed generally do not develop religious beliefs or practices involving the sun, the moon or the heavens; they are far more likely to have religious beliefs that focus on animals (either animals that they hunt themselves, or animals with whom they compete for food sources) or on their own ancestors and creation-stories. Beliefs involving the sun or the moon tend not to appear until the development of agriculture, when it is necessary to be able to predict the seasons well in advance, so that you can sow in good time, etc. This isn't an issue for seasonally nomadic hunter-gatherers; they simply respond to the environment as it presents itself to them and that works perfectly well.