With Parker or not, we are in position to go either way. We can bring in players along the way with TPEs, thus adding salary, or we could probably dump some players as others have said such as Schroder (who probably won't sign with us anyway) or JHern, who is not all that important and be under the tax for the season. I think it is brilliant that the Celtics have set themselves up with that flexibility.
To me it is strange how the NBA does it but if I understand correctly, tax is determined based on the team salary at the end of the season, not based on what you actually paid through out the season. So we could pay Al for the first half of the season but if we trade him at the deadline and take little or nothing back (not all that likely but just giving an example), our salary for tax purposes would be whatever it is without Al counted, even though we would have already paid him say $13M.
Trading Schroder for a pick for example to a team that has a TPE and needs a PG seems like a very viable scenario, if we decide to go that route. He will be a UFA in any case so we probably don't keep him anyway. Rules prevent us from paying above some limit where as other teams can pay him whatever they want.