Will an IC that requires an Oscillator work without one

Usually 32768Hz quartz crystals are used in the clock applications. This standard is very widespread and these crystals are cheap and highly easy to find.

In order to switch the clock to work twice as fast, you will need 65536Hz crystal, that is not standard, not so common and probably not so easy to be purchased. For example my local distributor has 32768Hz crystals on $0.1 each and the next frequency available is 1.8432MHz

Another possible issue is the work of the internal oscillator with the changed crystal. It will probably work, but some capacitors might need to be replaced with other values.

And at the end, the last possible problem is the stepper motor of the clock. Is it capable of stepping twice as fast as usual?

Have you consulted the data sheet? Usually when it does not do anything it is a config problem.

I have absolutely no knowledge on this but from PIC18(L)F2X/4XK22 Data Sheet.

Note 1: Quartz crystal characteristics vary according to type, package and manufacturer. The user should consult the manufacturer data sheets for specifications and recommended application.

2: Always verify oscillator performance over the VDD and temperature range that is expected for the application.

3: For oscillator design assistance, refer to the following Microchip Application Notes:

• AN826, “Crystal Oscillator Basics and Crystal Selection for rfPIC® and PIC® Devices” (DS00826)

• AN849, “Basic PIC® Oscillator Design” (DS00849)

• AN943, “Practical PIC® Oscillator Analysis and Design” (DS00943)

• AN949, “Making Your Oscillator Work (DS00949)

Looks like oscillator problems are common. So I'd start there. I know you have a prototype working, but if the right bit is not set no magic happens.

And:

FIGURE 2-6: QUARTZ CRYSTAL OPERATION (LP, XT OR HS MODE)

Note 1: A series resistor (RS) may be required for quartz crystals with low drive level.

2: The value of RF varies with the Oscillator mode selected (typically between 2MΩ to 10MΩ.

Or:

FIGURE 2-7: CERAMIC RESONATOR OPERATION (XT OR HS MODE)

Note 1: A series resistor (RS) may be required for ceramic resonators with low drive level.

2: The value of RF varies with the Oscillator mode selected (typically between 2 MΩ to 10 MΩ).

3: An additional parallel feedback resistor (RP) may be required for proper ceramic resonator operation.

Also from Making Your Oscillator Work

Question: I am trying to use a 4 MHz resonator with VDD at 3V. The data sheet allows this, but the oscillator does not work. What am I doing wrong?

Answer: You may be using the XT mode oscillator. When VDD is raised, the oscillator may start working. Select the HS mode oscillator instead. This will allow the oscillator to work at a lower voltage, but will also draw additional current. Alternatively, change the resonator to a crystal, use XT mode as before and check the loading capacitor selection. When making such a change, retest the oscillator circuit to ensure that it will perform as expected.

Not sure if this applies, but it did make me smile.

I'd also check my programming software to see if it actually is setting the config word the way you want, because I've run into system defaults on PIC's which were not what I selected. Oscillator selected but running very slowly because RC timing was the systems default. (OK I have some knowledge, just enough to make me dangerous - Good luck SSR).