Depends to some portion of the pen I would say. Some pens you might get frustrated with because the take a time to start up, others are just ready to go. Personally I store my pens with the tip facing up when they are inked. Hey, Brian G and many others told us so ;) No but seriously, some pens, like the TWSBI demonstrator looks crappy if ink gets in the cap and it gets a mess with the pens that do flow freely.
Having pencils lying down would most likely me 'more' safe and since there are plenty of pen stands that stores the pen lying down vertically - my answer is the same - check with each pen. For the pen you use every now and then and daily - might not be a problem but for me, I carry some pens to work in my backpack and having a somewhat mobile office. Having to start my day by dealing with ink stains isn't one start I need, so I might be overly careful.