yes, you can pull 10 normal gachas until you exceed your inventory (99/100 still allows you to pull 10)... and then if you really want to, you can empty your loot box of all the manyus you've been saving there. Of course, you can't do a mission until your back under your inventory..
I haven't gotten any 4 stars from normal gacha either.. although someone posted in another thread that they received a 5 star manyu in the normal gacha