Yes, it is still played on a hex grid. It would be possible to convert it to a non-hex grid format, but it would take a little tweaking.
The War at Sea ships are perfectly usable, if they fit on your hex grid. However, be aware that the WaS ships are from WWII.
Dreadnoughts, as the name implies, is focused on WWI. So you would either have to use the WaS ships as standins, or create the stats for the WWII ships. As you know already, creating stats for a Starmada ship is not difficult, and I'm sure you could get some help in these forums if you decided to do it.
Alternately, you could purchase actual minis to use with the game. (Which would be my recommendation.) You can get 1/3000 scale WWI ships cheaply here:
http://www.warweb.com/davco-13000-wwi-s … _1701.html
If you're not much of a painter and are willing to pay somebody else to do it for you, you can get that done here:
http://mywifepaintsbattleships.pbwiki.com/
You can get 3x1" bases for your 1/3000 scale WWI ships here:
http://www.litkoaero.com/
Or again, you could have it done for you at the same place you're getting the painting done.
This is an excellent source for beginner info on battles and ships of WWI:
http://www.worldwar1.co.uk/
It can help you with what the various ships are, what you can buy for various battles, and general inspiration. I've been doing this a little while now, and I am still out there all the time.
Finally. . .
You might also want to consider checking out Grand Fleets. Its like a more detailed, d10 based version of Starmada Dreadnoughts. If, as I have, you discover a love for naval wargaming, its IMO the best surface-combat engine out there.
Welcome, and let me know if you have any questions!