I dug around for a little bit, and it seems like the answer might be yes. Take what follows with a grain of salt, as I skimmed or read a few sources focused on different things and have done my best to reproduce a full picture.

First, some basic facts. Sponges anchor to the seabed (freshwater ones anchor to the dirt at the bottom of a lake/whatever). Sponge cells can move around each other and rearrange, part of their normal functioning, to keep water flowing through themselves efficiently for respiration and food capture.

Next, the mechanisms of reconstruction from a soup of sponge cells. As they bump into each other and recognize their own kind, sponge cells manage to hold together and hope for ground to attach to. They flatten out, presumably both to improve grip to the ground and to provide a large surface area for more cells to join. As long as the new colony ends up with enough of two specific kinds of cells (one makes connective mesohyl, the other makes everything else), it can grow.

The main thing I couldn't (quickly) find is specific confirmation that two healthy, stable colonies coming from a single halved source sponge can reattach, or if the reaggregation process only works following injury or during some kind of stress. Since the cells normally move around, though, it seems reasonable that this could work.

Based on all that and assuming their aren't other factors for sponge cells recognizing each other not entirely based on DNA, then presumably clones could also be attached.

Note that sponges don't actually stop growing. Their main limits are resource needs and predation, since some sea life likes to take nibbles or bites out of them (that's possibly a factor to why they are so adept at reorganization). So if your question involved cloning (rather than reattachment) only to get around a rough maximum size or early-life growth period that stops, it shouldn't be necessary.