Yes, you can upload your savegames from any PS4 game to the Cloud if you have a valid PS Plus subscription and enough space left to upload. Fallout 4 is fortunately no exception.
Sony also recently increased their Cloud storage capacity from 1 GB per system to 10 GB per system. In other words, you can upload 10 GB worth of save data for PS4 games, 10 GB for PS3 games, and 10 GB for PS Vita games, for a total of 30 GB across all PlayStation systems.
Considering that a Fallout 4 save game is approximately 5 MB in size (on PC), you could upload about 2000 different save files for Fallout 4 to the Cloud, so space shouldn't be an issue any time soon.
Just don't forget to save the game in the first place. Your PS4 won't be able to upload your victory against a Super Mutant Behemoth, if the save file doesn't exist in the first place, after all. Don't forget to configure your PS4 properly, so it can auto-upload those files too, unless you enjoy manually uploading them instead.
The game saves your progress automatically when you quit.
To be certain all your progress is saved correctly, be sure your character is located on the overworld (the map where you can move your character). Once you boot up the holotape once again, you'll have the option to continue your game:
Your character will be located outside of the tavern, where you started.
Best Answer
At the moment, there is no tool available to the general public that converts Fallout 4's PS4 saves to PC saves.