Is there an easy way to replicate this ceiling texture?
That is in fact a "sand finish", your intuition was right.

Now depending on the age of the house it could be sand added to the plaster, added to the mud, or a "sand finish" paint.   The last is your best hope of matching, as you would drywall it all smooth then simply use brushstrokes to recreate the pattern.  There are premixed sand paints amazingly enough.

When I've seen this done with wallboard mud, they have a mixer on site to stir every so often (the sand settles slower than blueberries).  A quick google search reveals a number of pros complaining about how hard sand finishes are to match.  Practice practice practice, on some scrap drywall.

Using a piece you cut off the ceiling for repair, try to figure out what layer the sand was added at (plaster, top coating on drywall, paint).