I can provide some general guidance based on common practices.
Whether a service center provides a pick-up facility for your bike would depend on the individual policies of that particular service center. Some service centers may offer pick-up and drop-off services as part of their customer service, especially if the distance to the service center is significant.
To find out if the service center for your Honda Unicorn bike provides pick-up facility, you should contact them directly. You can call their customer service hotline or visit their official website to check if such a service is available and inquire about the process and any associated fees, if applicable.
If the service center does not offer pick-up services, you might consider alternative options, such as using a towing service or arranging for transportation to the service center.
Remember to explain the issue with your bike in detail to the service center representatives so they can provide appropriate assistance or advice on how to proceed.