This can certainly be done, and you can choose when to fire off the email depending on how/when you want it sent,
Create an Action Rule instead of an approval process. Simply Test for the custom field to equal to the proper state in the Criteria tab. We have used drop down menus (pop-ups in WHD vocabulary) and tested for them to = "YES." From there, you can also add a status below for ANY conditions. For example, if you want to the email to go to the other team after your team has finished its work, you can add the criteria status = Completed. Under actions, send the email and include any of the custom field data you wish. The format is simply "<custom_n> = nth custom field."
You will have to know the "number" of the custom field as it is listed in Tickets > Ticket Custom Fields > Custom Field Display order. It is a small drop down field. REMEMBER, if you add custom fields, or change the display order, it will change this number!!! This means that if you change that number, the criteria test will still work in the Action Rule, but the data displayed in the email might change and no longer be useful to the receiver.
One thing we have done is to add custom fields to tickets that are only viewable by techs. This way, for example, the customer creates the ticket, the techs create the account and fill in the unique username or pin, for example. Once the ticket is closed, the email fires off to the target person with the custom field data so that they can then do whatever work is needed on their end. If the custom field is critical, be sure to make it required by the techs, otherwise the email might go forward without the crucial data.
Please let me know if this answers your question.
It is pretty awful to for the variable to be the display order. There should be a sequential value (that's visible in the GUI) after creating each custom field that never changes. No thought put into this feature...