Will it work? In my opinion no, It lacks any form of direction, personally myself I dislike the word summon. I much prefer use the term "call upon" and ask for assistance in what ever matter I may need guidance or help in.
You will need to have knowledge of your basics for trying to communicate with a spirit of your choosing.
Few things to ask yourself before even trying to this..is .
1) Whom or what do I want to communicate with?
2) Find out about about whom or what it is before trying it.
3) What are your reasons for calling upon them? (have respect for whom or what your calling upon, don't do it just because your wanting to play around)
If you have managed to answer all these questions satisfactorily to yourself then use your own invocation to fit in with your own requirements.
As to wither the crystal will still help, you will need to do a health check on it so to speak, check if it needs any clearing of energies done , It may have picked up negative vibrations over time, also you have not stated how the crystal came to be broken? was it an accident? or was it when it was being used for meditation? Healing? etc, these are important factors on how to understand what your crystal needs.
Maybe doing a spirit crystal spirit meditation would be more beneficial for you than trying to do a "summon anything spell" meditation on the spirit within the crystal will help you know the right thing to do for the benefit of your crystal and to what type cleansing it may need.
Love and Light