It's not a dumb question; it's actually the defining characteristic of performance for large systems.
In a shared-memory multiprocessor, all cores and all memory are logically connected along a massive shared bus, and both inter-core communication and regular core-to-main-memory communication takes up slots on the bus. In practice, of course, it isn't physically a single bus but a more complex topology (usually meshes, I think) with protocols that make it like a bus for cache coherency purposes.
One of the readily apparent consequences of interconnect is NUMA, non-uniform memory accesses. Historically (my information on this matter is a few years out of date, so I don't know how much this is true today), this has been a bigger issue for AMD than Intel, as AMD had wildly divergent memory latencies (2-3× between worst/best case) even for a 4-core processor. So if the OS decided to resume execution of a sleeping program on a different core, your performance might suddenly drop by ½ or ⅓.
For some benchmarks (such as classic SPEC, or make -j), multicore performance is approximated by running the same binary on every core and there is no sharing between different copies. The interconnect here matters only insomuch as the cross-chatter on the interconnect may impede performance. But HPC applications tend to be much more sensitive to the actual interconnect, since reading and writing from other processors' memory is more common (transferring halo data, or having global data structures that you need to read from and occasionally write).