Short answer is probably not. If the matter were part of a budget approved by the AGM, then yes, but you probably would not be asking if it had been explicitly approved by a general meeting.
If the tree really is damaging your property, then the OC could probably require the neighbour to remove the tree at their expense, not the OC’s, or otherwise remedy the situation. An arborist might be able to advise whether a root at the wall could be safely cut without destabilising the tree.
If the OC were to decide that the amenity of some of it owners would be improved by the removal of the tree, then perhaps the owners could agree at a general meeting that it would make an offer to the neighbour to remove the tree if the neighbour were agreeable and contribute to the cost. Since this would not be a usual maintenance item within the common property, then I don’t think the SC could just spend this money without explicit authority of a general meeting, unless, perhaps, if the case were obviously very good and the owners had been consulted to check there was a high level of support.