The answer is yes in principal. It depends more on your CPU & how much memory it can address,
For instance if it has the Intel® Core™ i3-2310M Processor Max Memory Size (dependent on memory type) 16 GB is the max memory.
Many laptop manufacturers quote a theoryetic amount of Ram however I have found in most cases it's the CPU's ability to address the Ram that sets the limmit.
According to Toshiba's specs for your laptop even though it may have come to you with a 32bit version of Windows that can only address approx 3.4 gig of ram the recovery drive is suposedly a 64 bit version of Windows.
If you right click My Computer icon, then click properties you should see your version of Windows & 32bit or 64 bit,
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