Yes, I expect that you will.
If a message cannot be sent as an iMessage (blue) for any reason - e.g. the recipient does not have an iMessage capable device, they have turned iMessage off, or you do not have a data connection over which to send it, it will go as an SMS or MMS message instead (green).
If the message is entirely plain text it should be sent as SMS, which are cheap or free on most mobile (cellphone) plans. However if it contains a picture or other attachment, which SMS does not support, it will be sent as an MMS message and these are usually charged at a higher rate.
At least on iPhone with iOS 9.3.2, you can see from the grey text in the message field before you start typing whether the message will be sent as iMessage or SMS/MMS ('Text Message'). If the recipient should be able to receive iMessage but you can't send one, e.g. because you don't currently have a data connection, sending should fail and you should then be asked whether to send the message as a text message or MMS.