What will likely happen if you were to define a LTM System in the wrong Data Center?

There is a real effect because Data Center association directly influences path metric calculations and load balancing decisions in GTM topology-based methods.

GTM can still communicate with an LTM regardless of which Data Center it is assigned to, as communication uses the configured IP address, not Data Center membership.

GTM uses the Data Center association of an LTM to contextualize the path metrics and round-trip time data gathered by big3d probes - if the LTM is assigned to the wrong Data Center, the topology and proximity calculations used for load balancing methods like RTT or completion rate will reflect incorrect geographic or network relationships, producing suboptimal or misleading results.

GTM can still resolve Wide IPs to addresses associated with that LTM because resolution capability is not gated on correct Data Center assignment.