Utilitech Linear Shop Light (Common: 4-ft; Actual: 4.55-in x 47.92-in)

Yes - They only use 0.7 amps each (80 watts). That would be 2.7 amps for 4 wired together. Should be no problem at all unless you have other things on the same circuit drawing power.

You're actually linking outlets since these have standard NEMA 5-15P plugs on the end of a cord. These are 80W max fixtures so figuring watts divided by volts they're pulling less than 1A. With a minimal #14 AWG wire on a 15A breaker with a 15A wall toggle switch you could easily handle four NEMA 5-15R outlets on a dedicated circuit. If your circuit isn't dedicated, you'll need to figure in what else is on your circuit to make sure an extra 4A won't trip the breaker. In the general area of my shop I have five fixtures on a 15A circuit connected to three-way switches when you first come in either end of the shop, along with another switch on that same circuit for one fixture over the laundry area (total 6 fixtures on the circuit, less than 6A maximum load). In the actual work bench area there's a second, dedicated 15A circuit switching ten fixtures (less than 10A max load). Then there's two fixtures switched off a third 20A circuit shared with the unswitched 13W dawn-dusk lights (one over each roll-up door), along with a switched 1000W flood over each of the doors if I need some real light outside (full load on that circuit could be around 17A so I needed to go with #12 AWG wire). Just do the math!

No, you can not link 4 of the Utilitech Linear Shop Light.