Yes. You can buy a car without a license. The driver of the vehicle will have to be named in the car insurance document which is known as the 'insured not driving policy'.
It is basically a declaration that you will not be driving the vehicle, and that you will contact the insurer if there are any changes in future.
You can find the document here: http://www.aig.com.sg/content/dam/aig/apac/singapore/documents/forms/non-driver-undertaking_letter.pdf