It will probably "run" it but I would expect a number of problems - especially if you are going to be making/using complex geometry/surfaces/mid-size assemblies.
Also keep in mind that recent versions (SW2014 and up) require 64-bit OS and should be running the Windows Professional version. Also, keep in mind that Windows 10 is only "qualified" for use with SW2016 or later.
Almost guaranteed to run. When travelling or on vacation I often need to be able to bring Solidworks up to answer questions on parts I have done, and don't want to bring my work Precision M3800.
So far I have had no problem installing 2015 and now 2016 on two different Dell Inspiron Laptops. One was an I3 with 8Gb RAM and integrated graphics and the other was an Inspiron 3137 with Pentium 3556U and only 4Gb RAM and integrated graphics. Both did have SSD's though. I've done this under both Windows 8.2 Home and Windows 10 Home. Amazingly, the second machine only cost about $300 + $120 for the 256Gb SSD, versus about $2K for a Precision M3800.
In an experiment, I have loaded assemblies of up to about 200 parts with no problems! It certainly isn't a screamer, but it works. Certainly a change from times past where if you didn't have the latest and greatest Solidworks was just a dog.
Depends on how you run SW on this laptop
You'd have issue if you use this laptop for design work; however, for design review with small assembly (<100), it might be ok