Yes, if a player is signed anytime before the end of the regular season, they should be eligible to be on the playoff roster.
But...
There is a deadline for players to be eligible for the playoff roster. If a player does not sign with a team before a certain date (we've established that date is in early March) he is not eligible by league rules to play in the playoffs.
I don't dispute it isn't fair to have a deadline for eligibility, but the fact of the matter is that there is one in place.