Yes, a 3–4 inch resistive touchscreen can normally be operated with a finger. It does not require a stylus.
However, it responds to physical pressure rather than just contact. A fingertip spreads the force over a larger area, so it may need a slightly firmer press than a stylus or fingernail. With reasonably large on-screen buttons, finger operation should be fine.
Resistive touchscreens do have a finite mechanical life because the upper film flexes every time it is pressed. The two conductive layers are kept apart by tiny spacer dots, so they should not simply stick together during normal use. On cheap or heavily used panels this can happen, but scratches, worn conductive coating, damaged edge seals, calibration drift and dead areas are more common failures.
Some other disadvantages compared with capacitive touch are:
* the flexible top film scratches more easily than glass
* slightly lower light transmission and contrast
* less pleasant swiping and dragging
* periodic calibration may be required, especially with 4-wire panels
* a thick protective cover glass cannot be placed over it because the surface must flex
* 4-wire panels can lose accuracy as frequently used areas wear
On the other hand, resistive touch still has some useful advantages. It works with gloves, a plastic stylus, a fingernail or almost any other object. It is inexpensive, accurate for small controls and easy to connect to a microcontroller, sometimes using only a few ADC pins.
That is why it is still common in Arduino projects and some industrial equipment. Mobile phones moved to capacitive touch because users expect a hard glass surface, very light touch and smooth multi-finger gestures. For a small, low-cost interface with simple buttons, resistive touch can still be a perfectly reasonable choice.