Yes,
Minas Ithil was still important in Third Age 2002 when it fell. It was strategically placed to control the only east-west pass into
Mordor. It was more or less due east of
Osgiliath, the original capital of
Gondor, and with
Minas Anor helped defend the capital from attack.
The siege apparently lasted about two years. If the
Nazgûl had
Orcs block the entrance to the valley, as I suspect they did (that’s how historical
sieges were conducted), then neither relief
armies from Minas Anor nor supplies could reach the defenders; and of course, they could not expect any help from east over the pass.
Though they did abandon the
Towers of the Teeth, the Dúnedain of Gondor did not give up
Cirith Ungol. Briefly deserted following the Great Plague of 1636, the Dúnedain reoccupied it. It was taken by treachery (
RotK, “
Tower of Cirith Ungol”) by the
Witch-king. We are not given any details, but it’s likely that was the opening move of the siege of Minas Ithil, since Cirith Ungol was its outpost. It’s likely that a warning beacon atop its uppermost tower could be seen in Minas Ithil, just as
Frodo and
Sam could see the dim light the Orcs kept. (The Dúnedain also kept warning towers along the north and south side of the
White Mountains:
Gandalf and
Pippin saw the northern
beacons being lit as they rode to
Minas Tirith.) We should suppose that its fall forestalled any warning of the impeding attack upon Minas Ithil.
Minas Ithil also controlled the
north-south road the
Númenóreans built in
Ithilien. The fall of the
fortress basically cut Ithilien in half. Besides leaving the residents of that beautiful strip of land open to attack by Orcs and worse things, it eventually gave Mordor control of the road, and ultimately access to the bridge over
Anduin, over which the Nazgûl crossed in 3018 to begin the Hunt for
the Ring.