I don't think so, nel...i looked st john's wort up and stared at a bunch of images, and it's not the same as far as I can tell. It's going to be warm outside here today, so I will go out and clear the weeds from around the bush and take a better picture.
I have looked at a series of different Hypericums, and I tend to agree Nel and Vienna...it looks to be a member of the St John's wort family...there are 9 genera and over 500 species in that family so maybe letting it bloom will give a definitive ID
Are the brown things the remnants of the flowers?
Look into some of the ornamental Origanums, such as Origanum libanoticum. Many Origanums have bracts around the flowers, and these bracts hold on for a LONG time, gradually turning brown. The flowers grew in between the bracts, but fade and fall off rather quickly.
~Fragrance is not a key- many Origanums have insignificant fragrance.
~Leaf shape varies among the Origanums- some are more rounded, some are longer.
These things are common among some of the Hypericums, too, so I am not ruling that out. Just suggesting another species to look into.