Developer with HCI background studying graphic design

I'm thinking about going to design school for a year, studying graphic design.

I want to get work as a UX designer/researcher, with the possibility of day to day activities like user research, user testing, user interviews, analytics, mockups, wireframes, working with clients/stakeholders, content hierarchies, contextual inquiries and so on.

I understand not every role would be this broad.

My background is ~3 years in systems administration/support, ~3 years as a web developer.

I did some postgrad study in UX (HCI) and was fascinated by the field and want more.

Many UX job ads I look at ask for designers first, often with design skills (layout, colour, typography, photoshop and illustrator) and UX skills second (user testing, IA etc).

Further to this, although I have some academic background in UX I don't see research-based roles appear very often. I am looking for work in Sydney. It seems to me that academic qualifications and knowledge don't get you that far.

Two questions:

Is the reality that most UX designers/researchers start in visual/graphic/web design and move into UX?

Does 'design thinking' and process (creative, collaborative) play a significant part of these roles and would you consider it valuable for the role I'd like?

Many thanks for your responses.