Yes, as you say, it means the phone number of the switchboard, you don't need to write anything else, the number is implied. You could write switchboard number if you want.
Telephone switchboard would translate as "conmutador telefónico", wouldn't it?

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Note added at 18 mins (2015-11-25 00:19:59 GMT)
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You can also write it as "main (phone) number".