Older light fixture with 3 bulbs - each bulb has 1 white and 1 black wire from it
In a word: Yes.
In a bunch of words: Yes, this is called connecting in parallel.
All household lighting loads and most appliance loads operate at the same voltage. So each lamp, fan, toaster, phone charger, etc. needs to be connected between one of the hot legs and the neutral bar in the service panel.
In the case of your lamp, each bulb needs its own separate connection to a hot (120v) supply and a neutral.
The circuit connection considerations of household wiring are very simple, and can be explained in a page of text. Two or three pages with the diagrams. The bulk of an electrician's work, and the content of the NEC, are concerned with safety.
Speaking of safety, you should use two wire nuts for your job. Different manufacturers use different color codes for the sizes, so you need to look at the chart on the packaging to determine the size to use to join one supply conductor to three flexible cords. There is a lot of leeway here. If you can get the nut onto the wires, then it's big enough, and if you can't pull any wire out of the nutted connection, then it's not too big.
(Personally I prefer the one-word answer but American schools have trained me to keep writing until the proctor says stop.)