SATA 2 isn't really a problem. Most people obsess over the max sequential speeds. Those actually don't matter much. A modern HDD will hit about 150 MB/s sequential read/writes, while a good SATA3 SSD will peak at around 550 MB/s. So the SSD is less than 4x as fast as a HDD at sequential speeds.
Where SSDs get most of their speeds is with reading/writing small files (related to IOPS). A typical HDD can only manage about 1 MB/s at 4k read/writes. A decent SSD will manage 50-70 MB/s 4k read/writes. Furthermore, if you enable NCQ on the SSD (allows it to read/write multiple files simultaneously without having to wait to exchange data with the computer), they can usually hit 200-300 MB/s at 4k read/writes. So they're hundreds of times faster than HDDs with small files. (Newer drives are starting to push 300-400 MB/s.) The IOPS reflects this as well. HDDs are typically 120-160 IOPS. Good SSDs are 70,000-100,000 IOPS. (IOPS basically measures how fast the drive could handle files one bit in size.)
Note that even with NCQ, the peak speed at 4k read/writes is right around SATA 2's limit. So SATA 2 doesn't really bottleneck 4k read/writes that much. The SSD will still be several hundred times faster than a HDD. The important thing is that your SATA implementation has to support NCQ. I think all SATA 2 chipsets support NCQ. Check your BIOS to see if there's an option for AHCI mode. AHCI is necessary for NCQ. (Note that you'll have to repair or reinstall Windows if it was installed in SATA mode and you wish to switch it to AHCI mode.)
Even without NCQ, the SSD on SATA 2 will still be much faster than a HDD at small files. It'll just be a several dozen times faster instead of a few hundred times faster.
Also, the MB/s scale is inverted from how we perceive speed. So the bigger MB/s gets, the less it actually matters. Say you need to read 1 GB.
■A 100 MB/s HDD will take 10 sec
■A 250 MB/s SATA 2 SSD will take 4 sec (6 sec improvement)
■A 500 MB/s SATA 3 SSD will take 2 sec (8 sec improvement, 2 sec more)
■A 1 GB/s PCIe SSD will take 1 sec (9 sec improvement, 1 sec more)
So compared to the HDD, the SATA 2 SSD actually gives you 75% the speedup of a SATA 3 SSD at sequential read/writes (6 sec faster vs 8 sec faster), even though its MB/s incorrectly implies it should give you half the speedup. In fact the SATA 2 SSD will give you 67% of the speedup of a PCIe SSD.
So yes, absolutely, you will see a substantial improvement switching that old laptop to a SSD even though it's limited to SATA 2. Also, when you upgrade laptops, you can move the SSD to the new laptop so it won't be like you're "wasting" the SATA 3 capability.