I would say no because enzyme activity does not only rely on the active site but also on the rest of the protein sequence. Since 1) it helps all the side chains of the amino acids involved within the active site to adopt the right conformation, and 2) it stabilizes the substrate and the product during the enzymatic transformation.
It is a common practice (although frowned upon by some) to prepare a construct consisting of only the catalytic domain of a multidomain enzyme and measure the catalytic activity. Truncation of the domain at the N- and/or C-terminus may also be prepared, especially if these regions are far from the active site.
Some common reasons for doing this may be to reduce the size of the construct to improve heterologous expression, to improve the chance of getting it to crystallize, or to remove a transmembrane or peripheral membrane domain so that the protein will be soluble.
In many cases, the catalytic activity of the protein is unaltered. However, allosteric effects may be altered. Also, if the substrate is a large molecule, such as another protein, significant interactions with the substrate may be lost. If the substrate is membrane-bound, releasing the enzyme from the membrane may have a significant effect on its interaction with the substrate.
Some things about the enzyme can be learned from a truncated construct, but the possible losses of biological functions should be kept in mind.