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I do not believe so. Currently custom fields are just barley there and not really that useful as there is no logic at all tied to them.
If you want to vote there are a few open feature requests to improve the usefulness of custom fields.http://thwack.solarwinds.com/community/tools_tht/web-help-desk/web-help-desk-feature-requests/content
You could do this through an "Action Rule" by modifying the ticket. So, if you have this custom field for all Request Types, you could just set it at ticket creation to modify the ticket and select '2' for your custom field for all new tickets. If it is only for a certain request type, you can narrow that down as well. If the '2' didn't apply for the ticket, your techs could just make the change when working the ticket.
I use custom fields extensively and use the "Action Rule" method referred to by robtyler. It works great. I have around 80 action rules for different uses of custom fields and couldn't do without them.