Does using a french press effect the taste of coffee vs the manual method? My normal method is put coffee in cup. Put some hot water for 30 seconds. Put remaining hot water for 2 minutes.

Strain and drink. 

Now if I buy a french press machine should I expect a change in taste of the resultant coffee?
In the case you are describing there won't be a big difference to French press, assuming that you are able to strain the coffee as well as you could with a french press. As long as you manage to strain it properly so that most of the coffee particles are gone the result would ceteris paribus be similar (which means same times, same pre infusion, same water and same temperatures, same grind size, etc.).

That is because the methods would be identical, they are both full immersion brewing techniques. In both cases you pour the water on the grounds, let it brew and strain in the end. There are many tips on how to improve your brews with these kind of methods on the coffee stackexchange.