I believe that you will have more benefits that constraints with home-grown support. And i really believe that the major benefit is that you can give your own train and transmit your thoughts and 'love' that you feel for your company. That's a step forward to create a team that can transmit that 'love' and customer care to the customers when giving support to them.
You can, in long term, outsource some of your support. But this 'outsource team' must have someone in site of your 'local' team' to control and monitorize.