Nope your current seals stay with the GC and will remain locked unless you rejoin that GC.

You will start in the new GC with 0 seals and need to earn them all again. But gear from the lvl 60 dungeons are worth 1k+ and if you are capped in your crafting/gathering jobs you get a ton of seals from those turn ins as well for the lower ranks and you will unlock that GC's hunt log which gives seals too. Recapping your seals can be incredibly fast.

The old ones will remain on your currency tab but will be grayed out. It's a good thing if you are like me and bounce between the GC just for a change of scenery now and then.