Yes, exercises can increase your range. Its not so much the particular exercise itself though thats going to do it; its the drilling and stabalizing of technique.
Basically, when you sing a song, theres too much involved. Your trying to sound good, sound cool, put some emotion into it, your not just singing on vowels like most exercises, the phrasing changes throughout so your breathing isn't really consistent, ect.
So, the smart thing is to do exercises, and focus on one thing at a time. When your doing a scale, lets say its a major scale consisting of 5 notes on the vowel "AH".
While you do this exercise, you are only focusing on one vowel, which is "AH". This vowel is good for opening your throat, relaxing your jaw & tongue, and working on placing resonance. Thats just 3 huge benefits on focusing on this 1 vowel.
The next big benefit is that you are only covering 5 notes at a time, and none of the intervals are too far apart. This lets you smoothly and slowly cover your entire range, and really focus on getting your notes down well. If the scale goes 1,2,3,4,5,4,3,2,1, your going to eventually get to a point where within the scale, you are changing registers. Notes 1 & 2 may be in chest, then notes 3 and 4 may be your break where your going into a 'mix', then note 5 will be either falsetto or head voice based on your development/tonality your doing the exercise in, then you go back down into that mix, and finally back into chest. If you can do this all while staying completely relaxed, you'll get through it. If not, you'll break and you can try again.
The other big benefit is you can focus on your breathing technique and support. Before each round of scales, you take your breath, expand your stomach and intercostals, and push down a little bit (or a lot if your doing this loudly in your higher registers). You don't always have that much focus in a song.
Once you get all these good habits integrated, your voice is going to unlock, and your range will increase in both directions quite a bit. Your almost always going to see a larger increase in high notes rather than low.
As far as myself, I havent checked my range forever so I honestly don't know, and im not warmed up enough to check right now. I will guess that it would be around C2-F#5. I can go somewhat higher and somewhat lower with more effort, but not with enough comfort or consistency to count it. The register those notes are in really just depenRAB on how much support and volume I put in it. It starts sounding a little thin and screamy around D or E 5 i'd say, depending on the day, but they can all be consisdered head voice. Its all just a style thing, I stick with more of a classic soul/R&B style, with some Queensryche/Priest styled vocals mixed in. This summer I will be working full time as a vocal coach and doing session work, so when I have that time available to me with recording, i'll have some stuff to post.
When I first started, I wasnt very good at all. I'd say I probably had maybe 2 octaves, probably under, but the voice was very weak with a sucky tone at that, so exercises have helped a whole lot.
Theres no amount of time you can put on how long it will take to increase your range though, because its very dependant on how much focused practice you put into it. If you focus diligently on what I said earlier in this post, it should come to you in a few months, a few notes at a time. If you obsess with range, it will never come because you'll always be focused on the note, and therefore you will tense in preparation for it and you'll be a lost cause. Once I finally quit doing that, my voice kind of unlocked and everything came together.
