Although I haven't seen anybody doing that. but I must first ask: what's the harm in doing it? A good presentation is all about making a commoner understand your work, experts would definitely understand the terms and literature. but a good presentation is always understood by the common people who will be present to attend the defense session. I had used some diagrams in my master's presentation. but I guess the best person who you should ask is your supervisor. And all the best for your defense.
Is it possible to use Hand-drawing to generate diagrams and put them in the thesis defense presentation?
See no reason why you can't - but some points you might want to consider include:
can your hand drawing pre-prepared in PowerPoint, Visio etc. software which can be more presentable, save you from nervousness / panicky situation while drawing during viva / defense presentation, save time especially your diagram is a complex one, ease better understanding of the examiners etc.
hand drawing during viva suitable for certain adhoc / impromptu clarification which you didn't expect / prepare in advance - hand drawing of your prepared research work during viva might give impression to examiners that you are not ready.
don't use hand drawing during viva to demonstrate your expertise or kind of "whiteboarding consultative selling" approach like some consultants do during presentation to customer because viva / defense presentation should be a pre-prepared structured session.
It would depend on the purpose, if you are showing your process - such as mind mapping - you likely should include it. If it is something that would better fit a table, chart or diagram then likely that would be the way to move forward.