Or in other words, how much work and money does someone has to do/have to have many SIM cards with many numbers, each loaded in a mobile phone.
There's three parts to this:
- Cost to legitimate users
- Cost to attackers
- Value you are protecting.
Losing legitimate users.
It has a cost to legitimate users. Sometimes the message does not get delivered in time, or at all. This may lead to some users turning away from the service. This is a loss to you; you have lost a potential customer or user.
How big problem this is depends on your service and user base. If it's a web shop with lots of competitors, this could be very real. If it's a professional service for the only of it's kind software, it's less of a problem.
Cost to attackers
Getting a new phone number will cost me 3-4$ and some time. If what I'm after is worth more to me than 3-4$, I will get a new SIM card. If it's to protected against automated spam bots on a forum and similar, it will be somewhat more effective, as the value of their registration tends to be fairly low, so they'll not go trough the hoops just to register on your forum software.
What are you protecting?
What are you protecting? Why is fake users a problem for you?
Broadly speaking, this could be to protect against their actions, e.g. placing fake orders at a web shop, or it could be protecting against spam. If it's effective will depend on if it's a targeted attack or a general, automated, attack. Targeted attacks that go after your website is much harder to protect against.