Excellent question—and one that’s important for all those who rely on service pokémon.
The truth is that, yes, evolution will actually improve a pokémon’s ability to perform. In your case, your growlithe’s senses of smell and hearing will be sharpened exponentially upon his evolution into arcanine, so if you thought he had an amazing sense of smell now, imagine having a pokémon who can detect panic attacks faster, the millisecond your breathing and heart rate change.
However, there is a price to it, and that’s the fact that while your growlithe may be two feet tall (assuming he is of average height), your arcanine will be over three times as large. For humans who live in rural or suburban areas or whose arcanine will also be helping with their partner’s mobility, it’s easy to take this difference in height in stride. However, for people living in urban areas or who otherwise can’t deal with the difference in size, evolving a service growlithe may result in more troubles than it’s really worth. You likely won’t be able to enter the same establishments or do many of the same things as you had when you just had a small growlithe by your side.
In other words, while evolving your service pokémon generally does enhance their abilities to assist you, always keep in mind that evolution brings about a physical difference that not many people can handle. It’s a good idea to do plenty of research into the changes that would occur to both your partner’s form and powers before going through with it.