No.
All the cable does is combine the video and audio into a single plug. No conversion is done. To get your VCR signal into a form (digital) your laptop can accept requires a video capture card.
Start by reading this link on how to PROPERLY (for those who'll jump in with their, But there's an easier and cheaper way suggestions) do a video capture. http://www.digitalfaq.com/editorials/digital-video/professional-analog-workflow.htm The only real difference is that in home video capture setup, a single VCR and a single capture device MAY be enough to do a decent/good job.
Then read this to see if your VCR is on the short list of recommended VCRs. http://www.digitalfaq.com/forum/video-restore/1567-vcr-buying-guide.html
And if you're interested and willing to spend the money for a known/proven good setup, check this post and contact lordsmurf for what you want/need: http://www.digitalfaq.com/forum/marketplace/8057-sale-complete-workflow.html
Keep in mind that you can recoup a good portion of your investment after you're done by reselling your equipment.
If you just have a few tapes to transfer you may consider letting lordsmurf do the work: http://www.digitalfaq.com/services/video-conversion-tape-to-dvd.htm
Why, lordsmurf, lordsmurf, lordsmurf? It's because he's one of the couple of handful of truly knowledgeable, honest and trustworthy members on VH and digitalfaq.com (which he's either a top administrator or possibly owner/creator of).
To be perfectly clear. I have absolutely no association with lordsmurf other than having the utmost respect for his knowledge and willingness to help others get the best out of their videos. As I stated above. Others may come in with cheaper and easier suggestions, but good/very good and cheap/easy are mutually exclusive.