Could a GTX 660 be installed in this?

The power supply might not be enough you need a 500watt minimum to run that video card. My answer is yes it could but you should get a better power supply because you are already getting a good deal as it is for that computer.

No. Assuming this is the product:
http://www.newegg.com/...6883108430
Slot 1: Low Profile, PCI Express 2.0 x16 (75w max)

Power supply can't support cards that require a direct connection to them. GTX 660 requires a 6-pin connect to the power supply. The power supply can't handle a GTX 660, and upgrade of power supply is probably next to impossible to find one that fits and supports an over 75 watt card.

The best you will get into it is GTX 750 low profile.
Something like this:
http://www.amazon.com/...B00JB1XJ4S
Change to low profile bracket.
http://www.anandtech.com/bench/product/1039?vs=1131

Note the CPU is Intel Core i5 650 (3.20GHz)
Passmark 3144
https://www.cpubenchmark.net/...u_list.php
Pentium G3220 @ 3.00GHz 3191
Not an especially fast CPU, but the system price is cheap.
Should have 2 slots available for ram, but you need to open it up to figure out what ram, or try crucial.com.
Should be upgradable to 8GB RAM.
Pretty sure this is the motherboard
http://www.ctsestore.com/ibm-lenovo-thinkcentre-m90p-socket-1156-motherboard-71y5975-5391-sff
Single width graphics cards only.

DEFINITELY 100% Sure NO GTX 660.
Probably low profile GTX 750 pushes the system to its limit.

Not sure if the board is a custom size.