The real answer to this question is a little greyer than "will it or won't it work". I'm an electronics engineer and know a little about batteries. Essentially the AC adapter that ships with your laptop is rated to a maximum output of approximately 150W (19.5V x 7.7A). That does not mean that your laptop requires 150W of continuous output to run necessarily. Consider that the AC charger was engineered so you can both run your laptop at full speed while simultaneously charging the battery. On top of that there will be a lot of variance in how much power your laptop will consume based on engineering tolerances, the power saving profile and the activity that you are performing. Things like heat will also affect power consumption.
So there are a number of scenarios that could happen if you were to plug in a 60W max rated external battery into your laptop that usually takes a 150W AC/DC adapter:
1) Everything works 100%. Why? Because the real power consumed by the laptop is a lot less than that for which the AC adapter is rated.
2) Everything works almost 100%. Why? Because you are tanking charge with the built in battery which is making up for the sub-standard output it is receiving from the external battery. This means that you can't run your laptop off the external from empty but you can run it okay when you have charge only to find your laptop battery is still discharging only at a far slower rate. This is the most likely scenario, akin to what happens when you are using your phone contentiously while it is plugged into a computer's USB port as opposed to a wall charger.
3) It does not work. This could be due to a safety mechanism in the external battery which instead of limiting the amount of current it outputs it shuts down the output when an external load tries to pull too much current. This is what happens on some older (or even newer) aircraft in seat chargers. Try plug a 17" gaming beast into your local 110V airplane seat and most likely it will appear as if it is charging for a moment and then shut down.
4) It does not work ... for another reason. Remember the laptop manufacturer engineered the thing to expect it receive input current from the AC adapter it shipped with the laptop. That means the electronics in the laptop may say something like "oh I'm plugged into a wall therefore I should be able to charge my battery at this rate and run all my internal components at full speed". This is not likely as manufacturers really should engineer there stuff to be smarter than that.
5) It barely works. With your laptop turned off you can slowly charge the internal battery from the external one, for the reasons above.
6) Maybe you can get it to work. Play with your laptop's power settings and make sure your internal battery is charged while you are using your external battery.
Best advise is to speak to people who are using the same model laptop as you with the same model battery you intend to purchase.