Yes, it will see a 1TB as it's boot drive. Not talking external, which is of limited use.
With the PS3 slim, "Advanced Format Drives" are not an issue.
However, it will not format a boot drive bigger than 1 TB. I tried.
I used a SATA to eSATA PS3 extender kit. (see link)
Using an external drive as a boot drive is achieved with a POWERED eSATA enclosure.
I tried a eSATA cable powered unit, did not work.
Anyway you don't want the new drive to over tax the PS3 PSU.
Also, it will not add to console heat, I am guessing lengthening the life of the console itself.
If you don't want to go this route, any laptop,hybrid, or SSD 2.5 drive 1 TB and under will work.
I had a 500GB 7200 rpm laptop drive in before the upgrade with no adverse effects.
Some have warned against heat and power requirements of 7200 rpm drives over 5400 drives.
For the enclosure I ended up using a 1TB 3.5" Western Digital AV-GP drive., designed for always on use.
An enterprise server drive might have been quicker. I would recommend a desktop drive over an enterprise drive due to the fact I keep the enclosure always on for convenience.
Everytime I power on the PS3, it's already fully spun up.