No. The Mamluks were determined to get rid of them entirely so they would stop coming back. They didn’t want a repeat of 100 years earlier, when the crusaders managed to hold on to Tyre, which was then used as a base for the Third Crusade to regain control of Acre and the rest of the Mediterranean coast.

The Mamluks conquered most of Acre on May 18, 1291, and took the Templar fortress in the city on May 28. By August, the Mamluk had taken all the remaining crusader cities and castles. They destroyed their fortifications and expelled all the European Christians who hadn’t been killed or sold into slavery first.

Although the cities were eventually rebuilt and repopulated, this war was temporarily devastating for the coast:

“The political victory of the Mameluks was won at the cost of the destruction of the ancient Syrio-Palestinian city civilization. In1333 Jacob of Verona wandered sadly through the deserted ruins of the coastal cities. Only the ruins of palaces survived to tell of former splendour. The city walls had collapsed and within their perimeters there was no one except a few Saracens living in the most primitive conditions.” (Mayer, pg. 274)

Maybe about 100,000 people did escape back to Europe. First they went to Cyprus, the only remaining crusader state in the eastern Mediterranean. The Kingdom of Cyprus lasted until 1489, when it became a Venetian colony, and wasn’t conquered by the Mamluks until 1571. But in 1291 this massive influx of refugees was an enormous economic and humanitarian crisis.

At the time they thought it was just a temporary loss. There were plans for new crusades, but it would be much more difficult without foothold on the coast. The Templars tried to invade the mainland in 1299-1300 but they failed. Attempts to ally with the Mongols against the Mamluks also failed. European powers were mostly uninterested, since crusading in the Near East was clearly unsuccessful in the long run.

Merchants were still allowed to travel and trade in Syria, and Latin Catholic religious communities were allowed back in the 14th century, but the Mamluks ensured that no Catholic political/military presence was ever allowed there again.

Sources:

Hans E. Mayer, The Crusades, 2nd ed., trans. John Gillingham (Oxford University Press, 1972)

John France, ed., Acre and Its Falls: Studies in the History of a Crusader City (Brill, 2018)

Christopher Tyerman, God's War: A New History of the Crusades (Penguin Books, 2006)