Yes, those rigid elements may affect your results.
CAESAR II allows unconnected piping. By default, each subsystem (defined by unique sets of node numbers) will share the same origin (0,0,0). The analysis will be fine but the plot will be disorienting. You can use the global coordinates tool (also listed in the Edit Menu item) to reset the plot location of the starting point of each subsystem.
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Dave Diehl