Depends.
First, the theory:
If the adapter gives the same Voltage output at the same Amperage and Frequency etc., then yes, the knockoff model should work.
Now, the reality:
1. Will the knockoff model give the same output that it says it will? if it gives too high it could blow the laptop.
2. Will the knockoff model work for more than five minutes?
3. Will the knockoff model work for more than five minutes without catching fire or something?
If the knockoff isn't claiming to be made by the manufacturer, and it actually has a make (aka isn't some dodgy unbranded thing), then it's PROBABLY ok.
Personally, I would be rather cautious buying something like that from a thrid-party, but many of them are fine. If the "knockoff" is an "alternative" (as in not actually a knockoff, just an innocent third-party addon), then it may well be ok. The safest bet is to stick with the manufacturer.
I would suggest looking up the make and model of the "alternative" on google, and seeing if you can find any reviews (preferably customer reviews).
