While everything you said electricpete is spot on, I'd have to say that for the average user, it's not going to make a difference performance-wise. I consider myself a pretty average user with about 120 apps installed, phone use, texting, facebook, a little twitter, some youtube, etc. during the day. Maybe some map use ... oh, and a LOT of Android Forums
. Adding another service shouldn't be noticeable.
As for the ops question, a text blocking app will pretty much just sit there until a text is received. Sure it will eat a bit of resources, but if it's a well built app, I doubt you'd even know it was there. Check the reviews and if there are lot of complaints about slowdowns or battery draining, move on to the next one. Now, if Verizon now offers it as a subscription feature, they are blocking it at the network level and your phone will never see it. An app OTOH might actually receive the text, recognize that you don't want them from that sender and delete it without you ever seeing it. Again, you'll need to do a little due diligence to make sure it's what you want.