Yes, and no. Necessary, but not sufficient.
Architecture Office (AO) in particular is very strict & diligent about their patterns and practices. They are empowered & responsible for governance (in a good way), and rationalize (harmonize) efforts in the organization. The architect feels a belonging to this team to derive rules & priorities; and contribute/influence the big picture.
Agile (scrum) teams in particular have high cohesion. They disown anybody that don’t work with them in their pods. In spirit, of an empowered team, they want the team to make decisions, and hence, the architect must belong to them. This is the best way to influence work that happens on the ground.
X-Functional Leadership teams are typically composed of program, product, operational, business, architectural, manufacturing and engineering points of contact. Teaming with such a x-functional group is very critical to the success of a x-functional initiative.
Each team is a mission focused team. Each team is empowered. Each team is connected to other teams (team network grid) for information flow & communication.
The architect (and other titled roles) find themselves to be part of several teams. I have had architects tell me that they see the “scrum role” as solid line, and “AO” or “X-Functional LT” as dotted line. Some others tell me that “AO” is solid line, and “scrum role” or “X-Functional LT” is dotted line. i.e. in essence they are prioritizing a team to either spend time or to trade-off a quality attribute. It’s not just navigating a matrix, but a network of matrices. Trading off – Authority & Influence. This can become complex.
If Architecture is the art of managing complexity, and complexity is due to structure, then the ‘architect’ has to play in space between spaces. (S)he has to be in different teams. Given the nature of the complexity, sometimes, (s)he has to play devil’s advocate with the scrum team, and sometimes with the “AO”. (S)he has to own the architectural decision, that (s)he is responsible for, through transparent communication. (S)he has to make all such teams believe/perceive that (s)he is part of that team.
Being part of multiple teams is a reality. Different leaders pulling in different & sometimes conflicting directions is also a reality. Being part of multiple teams is an opportunity to influence & carry information. The last thing that should happen is to lose your mind trying to do everything. It’s best to plugged into each team, make them believe/perceive that you are working for them, however, focus on one thing at a time. Multiplexing is like an adult choice.