When I log into my unix servers, I get an xterm window and usually open several more from that initial one. Is there any danger in closing the first window but keeping the children windows open?
Generally: no worries about closing the first window.
Tell me more specifics --
Something about how you phrase your question implies that you're launching non-graphical production processes by using X11. If the things you're running don't require a GUI, I'd recommend against running the GUI to launch them. Read about GNU Screen and/or nohup.