There's a couple things to consider here. Short answer- yes, I think you should get a tune. In my opinion as soon as you go RHFC it's time for a tune not only for gains but also because now the car is breathing much differently from stock and it needs to learn how to balance fuel-air ratio gain. That being said, if you plan on getting a catback in the near future go ahead and do that first because a tune should be your last stop so you don't have to do it a second time.
To that end, your mechanic is right, the cats are the most restrictive part of the setup. Adding a catback will help with the exhaust note and perhaps add a handful of hp but nothing huge. I disagree with the above poster saying all you've done is add noisemakers. HFC are the most bang-for-buck bolt on mod for our cars.
CAI are without a doubt a better choice than short ram, but again, we're talking a handful of horsepower that most likely won't even notice. And again, if you are going to switch to a CAI in the future wait to get a tune until you are done with bolt ons.
The honest truth is our cars just don't make very much power gains off of breathing mods. We're talking about finely tuned Jap V6s not LS powered cars. Without forced induction you need to be fully aware of what these cars are capabale of so as not to disappoint yourself. Here is a link to my thread after I got tuned. https://www.myg37.com/forums/g37-cou...ned-today.html
Bolt ons include R2C short rams, Fast Intentions cat back, and fast intentions RHFC. I have an AWD coupe so let's assume 25% hp loss from the crank to the wheels (I'm being generous to myself here) and say stock hp number is 248 (rounding up). After all my mods I was sitting at about 274 wheels horsepower. An ECUtek tune took me up to 290hp on a 100 degree day so maybe under normal conditions 293-295hp. It's up to you to decide whether all the money is worth it to you as only you know your finances and how important this is all to you. Your car might see better gains than mine, who can say?
There are other benefits to tuning though. Depending on the tuner and how involved you are in the process you can dial in the car to how you like it. My tuner was able to get the power and torque curves much more linear so I have better power throughout the RPM range. Some people say ECUtek can clean up the shift lag on AT cars but mine is pretty much the same, that's something you'd have to discuss.
Long story short, finish up your bolt ons and then get a tune. IMO a cat back is worth it for the noise and couple of hp. I wouldn't change a thing about my FI setup. That being said, I'm pretty bored of the 290hp and am thinking about moving on to a V8. Your mileage will vary depending on what you want out of your car. Hope this helps bud and good luck.