Yes. The signal at the pin goes to two places, delivering to them the same voltage.
Where they part ways physically is unimportant over the small distances these are probably, and is mostly something you can decide on the basis of convenience.
For getting into the Arduino board, you could use a male Dupont jumper, or a pin header you could solder a wire onto.
They are inexpensive. Long pin headers are easily cut to size - I'm still working through a life time supply of 40 pin headers I got some years ago - never mind how long precisely.
The Dupont jumpers can be cut, and used in the gazintas on the UNO board. Cut they are handy to solder to a few parts like switches and stuff for easy rapid testing.
When tou are doing the other side, where the power is being delivered through the MOSFET the important thing will be wire of a good size and solid connections. You can run this circuit on a bread board but it would be a stretch for that, and def not the way you leave it when saying this is finished.
Small circuit boards with a grid of 0.1 x 0.1 "pad per hole", um, holes is an easy way to,lash up a tiny circuit like this.
HTH
a7