No. Different versions of Vegas Pro can exist quite happily on the same computer.
But be aware that some FX extras that may have shipped as part of a bundle with a previous VP version may not work in VP17 because many of those FX extras are license-locked to the VP version that they came with.
I assume then if I need the disc space I can delete 16 from my desktop?
Yes, absolutely.
I then load 16 to my laptop?
Yes, absolutely. You can have Vegas Pro (though not VP 365) installed and activated on 2 devices at the same time. Nonetheless, it may be worth de-activating the current installation of VP16 from your current computer before uninstalling - or you can do that via My Products on your My Account on Vegas Pro's website.
"How many computers can I use VEGAS Pro on? You can use VEGAS Pro (14.0 and later) simultaneously on 2 devices. There are 2 ways to deactivate a device so you can activate a different one:
Visit your MAGIX account > My Products > Show More Details > Deactivate. This option can be used only once a month.
From the VEGAS Pro Help menu choose Deactivate the Software on this PC. This option can be used as often as you wish. An internet connection is required."