Follow Up Email for Digital Apprentice (Marketing)

I recently (just under a week ago) undertook an interview for a digital apprentice for a UK based marketing agency.

From what they told me during the meeting, the role would generally involve logging client tickets on their internal support platform, and relaying various bugs/fixes that would be needed to the design & development team.

They also mentioned that they would be looking to grow their social media presence. Whilst I wouldn't be directly working on that project, they said that they would want someone who would be proactive, and be able to help out and pitch in ideas when needed.

My question is:

Would it be in my benefit to send an email to the agency, saying that I appreciate their time and what have you, and that I also have some ideas on how they can improve their social media (which I do)?

Would that be too forward, or would you think that this would be something that is welcome?

Thanks in advance!

A thank you email is always appreciated. Show your enthusiasm for the position, and for the flexibility it will offer.

Don't talk (or even give a clue) about your ideas until you get the position. Then you can work on your ideas with inside knowledge of what the company really wants to do, instead of guessing based on an outsiders viewpoint.