Sort of. As you already know, God doesn't want to force anyone to be in Heaven or Hell. "Persevere to the end" means obeying God's commandments and overcoming trials/tribulations continually to the end of your mortal life on earth. When Jesus said, "He who perseveres to the end will be saved" (Matt. 24:13), He wasn't speaking just to those alive on earth in His presence, but to all those in the future in this world who would hear these words. And, He did not begin by saying, "But he who is saved and perseveres [...]" nor "But he who is unsaved and perseveres [...]" because it's only at the end of every person's mortal life on earth that they learn if they persevered in obedience and overcoming the tribulations/trials on earth or not, and thus reached eternal life in Heaven or not, which is why He said "But he who perseveres [...]".
Now, Jesus, being God, is eternal and omniscient, and thus from eternity has known who will and won't be a future inhabitant of Heaven, even before they were born. Regarding those He knows who will be future inhabitants of Heaven, they are not so because He has given them every means of becoming glorious and blocked all dangers of the devil, the world and the flesh. That would clearly be unjust. God gives them what He has given everybody. They use God’s gifts with justice, and therefore win future and eternal glory through their own free will.
God knows that they will reach this eternal glory. However, they do not know it, nor does God tell them in any way. The special gifts themselves are not a sure sign of glory; they are a more severe means to test a person’s spirit in their will, virtue, and faithfulness to God and His Law. God knows. He is happy to know in advance that a particular creature will achieve glory just as He suffers knowing that another will freely achieve damnation.
However, He does not intervene in any way to force the free will of any creature in order for it to reach the place where God wants everyone to reach; Heaven. Of course, a creature’s response to divine help increases its willpower. God opens up the more a man loves Him in truth; the love of actions, not that of words.
And again, the more man lives a just life, the more God communicates with him and shows Himself to him. It’s a foretaste of that knowing God that makes the saints in Heaven so happy. From this foretaste comes an increased capacity to want to be more perfect. However, man is always free to follow his own will and if after reaching perfection, decides to renounce the good done and sell himself to Evil, God leaves him free to do so. There would be no merit if one is forced to do something.
To conclude: God knows from eternity who are the future eternal inhabitants of Heaven, but man with his free will must want to reach Heaven using the supernatural help that the Eternal Father gives every creature. It will be like this until one’s last breath, whatever the gifts received or the level of perfection reached.
Remember nobody has ever arrived until their journey is finished. That is, no one can be sure to have merited glory until their time is over and immortality begins.
