Yes, from reading the first NHC Advisory just posted, it appears to be a fully qualified, pure warm core tropical system. Thus, Tropical Storm 'Alberto' has indeed formed, and a stone's throw from shore at that!

SATELLITE...RADAR...AND SURFACE DATA INDICATE THAT THE SMALL SURFACE LOW LOCATED OFF THE COAST OF SOUTH CAROLINA HAS ACQUIRED THE CHARACTERISTICS OF A TROPICAL CYCLONE.

And strengthening IS expected, at least in the near term ...

ALBERTO IS SITUATED IN A MARGINAL THERMODYNAMIC ENVIRONMENT FOR STRENGTHENING ...

It appears that the convection has not quite yet wrapped entirely around the LLCC, but continued returns from the Wilmington Doppler radar suggests this IS occurring, right before our eyes, and would eventually lead to the formation of a Central Dense Overcast (CDO) over the LLCC, nearly always a harbinger of further intensification.

THE LOW-LEVEL CIRCULATION IS A BIT TO THE EAST OF THE COLDEST CLOUD TOPS AND THE CIRCULATION CENTER SEEN ON RADAR.

A TROPICAL STORM WATCH COULD BE REQUIRED FOR A PORTION OF THE COAST OF THE CAROLINAS THIS EVENING.

Animated Doppler Radar Loop out of Wilmington, North Carolina:

Wilmington, NC Dopplar Radar Loop

Finally, of interest to note:

ALBERTO IS EARLIEST-FORMING TROPICAL STORM IN THE ATLANTIC BASIN SINCE ANA IN 2003. THIS IS ALSO THE FIRST TIME THAT A TROPICAL STORM HAS FORMED BEFORE THE OFFICIAL START OF THE HURRICANE SEASON IN BOTH THE ATLANTIC AND EAST PACIFIC BASINS.