No, that 3-in-1 adapter will not drive multiple monitors.
What you need is either a system that combines 2 monitors, or a system that chains them. While DisplayPort allows for daisy-chaining displays, this only works on supported hardware. This means your monitors need to both have two DisplayPort connectors and official support from the vendor and inside in the chipset to make this work.
I believe that you aren't going to buy two expensive chain-able monitors since, well, you don't want to buy an expensive adapter ;-) The next stop would be stuff like Matrox's DualHead2Go. That is a device that allows 2 displays to be connected to a computer as one big display. http://www.matrox.com/graphics/en/products/gxm/dh2go/digital_se/
It does cost quite some money, so it might be in your category of 'expensive adapters'...
The problem with your question is that it is rather specific. It's a niche that most people don't even know about, and not a lot of sales or development is happening there. While it could probably be done cheaper, there simply aren't a lot of options here.
Just remember: one video port can only ever drive 1 display, unless it's a daisy chained display port system or a device that turns 2 screens into 1 big virtual screen for the video port. There is no cheap 2-in-1 adapter to make this happen.
Small addition: you might be able to solve your problem with a USB DisplayLink adapter if you do not need 3D video or accelerated 2D video. It's a video card with a USB connector on one end and a video port on the other. It won't be fast or high-performance, but if you simply want more desktop space, it might work for you. You would end up with one of these: http://www.displaylink.com/shop/adapters
The MBA GPU may be limited to a single external monitor, but the USB to HDMI requires a driver installed on the MBA and that video/image is not using the GPU, it's using the CPU. So the limit is bypassed. Now it might be more complicated than this, but I think is this the basic premise. Be aware that for fast moving videos or games the USB connected display may disappoint. Also if the MBA is running near 100% CPU usage and then you add this USB display it may also disappoint.
If you looked to add more screen for email, YouTube it's likely to be fine. The hub might be more of an issue, if the cable is USB 3 make sure the hubs too
Best Answer
With an MacBook Pro Early 2015 you can connect two display using Thunderbolt 2
or one display using Thunderbolt 2 and a second one using HDMI
So in your case you need a Mini DisplayPort to HDMI adapter for a second HDMI display. If you want to use display with a higher resolution you need to get another adapter (DVI, DisplayPort, etc.).