Not if you do it right.
First, pick up the conversion manual from Jags That Run (JTR)
http://www.jagsthatrun.com/Pages/Datsun_Z_V-8.html you can also get it at a discount from Summit Racing
http://www.summitracing.com/
Next, while you are waiting for the manual to arrive, stop over at the Hybrid Z site
http://www.hybridz.org/ and check out those that have converted and ask any questions you might have. You also should check out Pete Paraska's awesome conversion site
http://members.home.net/pparaska/ Great stuff there!
Now, to answer your specific question, provided you use the JTR method and light weight parts, the steering will actually lighter and the car will handle better.
Why? Because with light weight parts the 350 small block Chevy (SBC) will weigh no more than the L6 engine you removed. Since it is only four cylinders long it will now be completely behind the front axle. This will change the stock weight distribution from 52% front - 48% rear to about 50%-50%. Also, the V type engine is much lower than the very tall L6 so the center of gravity for the car will lower and that will help to improve the handling as well.
Done right it will almost look and run like Nissan engineered it that way. Best of all is that it will also be very, very fast.
Good luck.
BTW, here is a couple of pics of my 1971 240Z based 1962 Ferrari 250 GTO with a 327 Chevy in it.
http://www.ofoto.com/BrowsePhotos.jsp?UV=969766190741_80589458103&US=0&collid=49144495103