It is a noncovalent (and therefore reversible). Remember there are no absolutes in biology as you seem to want to believe- so generally think of it as noncovalent.
In cell biology, "binding" of one molecule to another is nearly always non-covalent. An exception is enzymatic reactions where transient intermediates form.
However, certain protein modifications, which can occur on allosteric sites, are covalent modifications (such as phosphorylation); this would not be referred to as "binding" of phosphate to the protein- it would be called a covalent modification or post-translational modification. Protein modifications (ie: post-translational modifications) are not, strictly speaking, considered allosteric effectors (which refers to diffusible molecules that non-covalently associate with a site on the protein that is NOT the active site to modify the enzymatic activity of that protein).