yes, they can. If you advance into combat that hasn't been resolved yet, the advancing unit joins in and the combat is resolved next.
An advance might initiate a new combat engagement, it
might bring the advancing unit into an existing
unfought engagement, or it might bring the advancing
unit into an engagement that has been fought but
which remains unresolved.
If advancing into an existing unfought engagement, the
advancing unit fights as part of the engagement that
turn. This means the unit fights in two separate
engagements during the same Combat phase and could,
potentially, fight up to four rounds of combat during
the turn.