If the fountain pen has any kind of (suction) pump, then you will need to use the said pump.
The capillary effects alone will not have the power to fight the weight of the ink itself.
My personal hack
I have a fountain pen with one-time-use cartridges. It came originally with a very long one (compared with what is usual in shops). Because I did not want to purchase so much plastic (the small one time use cartridges), I decided to use the original one. To refill it I use a syringe (dedicated specifically to this purpose) to transfer ink from the ink bottle to the cartridge. I use it in this way for more than 20 years without any issue. The original cartridge, even though it was designed to be one-time-use, still fits properly, without leakage, to the pen.
Fountain pens won't automatically suck up ink when you dip the nib. You'll need a converter (cartridge) for your fountain pen.
Once you have the converter, it depends on what kind of converter you get: some have pressing pumps to suck up the ink, while some are twisting converters. By dipping the fountain pen nib into the ink bottle, you'll be able to suck in the ink by pressing on/twisting the converter.
This website has a lot of guides for fountain pens.
The answer is no. Since there is nothing that would suck up the ink, or something that would pull the ink in (like suction) the ink would not fill up the pen. Thats how gravity works btw. There are pens that have disposable cartridges, some have built in refill pistons, an some can use a converter, and some are vacuum (suction). The disposable cartridges are pretty straight forward. Unscrew the pen, pull out the old cartridge, click the new one in. There you go. Pistons and vacuums, and squeeze are similar because they all use negative pressure. For the piston, put the nib in a bottle of ink, then twist the back end. The piston inside will move up the barrel, and pull the ink in. Vacuum are similar. Pull the back, then dip in ink, and let if fill. Squeeze work by squeezing the ink chamber which makes the inside smaller, then hold it in ink, then release pressure on the chamber, and it sucks in the ink. There are many converters that work on different pens that perform all the actions listed above, so mess around a little and find what you like the most. Also, if there isnt a cartridge for the color you want, you can always refill a used cartridge with a syringe and use that.
Can a fountain pen suck up the ink into its reservoir if I simply dip its nib into the ink?
It depends on the type of fountain pen you're using. Simply putting the pen nib into ink will not fill a pen unless it's a rare capillary filler, like the Waterman X-Pen or Parker 61. Most fountain pens require some mechanical means of sucking up the ink; typically a squeeze mechanism of some kind which can exchange air for liquid.
If the pen is a cartridge filler, you'd need to swap in a same-sized/shaped converter for the cartridge.
If the pen has a built-in filling system, it needs to not have any leaks to work (may be an issue with vintage pens where rubber guts may have rottened or hardened, or plastic fillers that may have cracked with time). General advice: don't try to fill an antique/vintage pen until you know it's in operational condition: you can easily break Waterman lever boxes by forcing the lever against a petrified rock-hard rotten rubber sac.
Most modern cartridge-fill pens are tip-fill, where you only need to partially submerge the nib in ink to fill, but most vintage pens are not (Sheaffer snorkels, which have retractable ink-intake tubes, aside).
Older vintage fountain pens that use rubber sacs (e.g., a Waterman 52 or 5; or a glass-nibbed Spors) actually require that the lower edge of the section contacts the ink, so the entire nib needs to be submerged. The section is the hollow tube into which the nib and feed are friction fit and that the barrel screws on to. It's where you typically grip the pen. This is why some ink bottles (like the Shaeffer Skrip or Montblanc) have a smaller well you can fill by tipping the bottle, so that you can get enough depth to fill when the ink level is low in the bottle.
In addition, rubber sac filling pens require time for the rubber to "recover", so after you apply/release pressure, you need to wait 10 seconds or so for the pen to fully fill. With some piston and button fill systems (e.g., Parker Vacumatic), you have to press and release multiple times until the pen is full.
If your vintage pen is pre-1920s (say an 1890s ink pencil stylograph, or a 1910s safety pen) it's unlikely it has a built-in fill system, and is probably an eyedropper filler, where you have to unscrew a cap/end and use an eyedropper to fill the barrel.