Yes, you do have this option. From the main POP Peeper menu go to "Tools" > "PPtweaker...", then in the "Misc" options window use the 3rd drop-down option "When I single-click on tray icon" to select the option "Open POP Peeper" instead of the default "None" option.
Example:
From main PP menu - Go to Tools/PPtweaker to change the option above as pointed out.
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