If I have two connections to the Internet (one via
eth0 and the other via
wlan0), will both be utilized by default?
...or do I have to make some adjustments in order to have applications take advantage of both connections?
The short answer is no. A PC has only one given default gateway and that's used for all traffic. You might still see some packets in/out of the secondary interface, but it'll be layer 2 stuff, not IP based.
netstat -r to see what direction your traffic is taking.
The longer answer is "no, but you can bond your interfaces together, creating a "virutal interface" which is capable of using both cards". Basically, follow one of the links mentioned in your comments. You'll need the ifenslave package and a guide on how to configure, such as the ones I mention in this answer.
Actually you can combine 2 or more disparate internet links using Vtun and multi-link PPP see http://johnlewis.ie/bonding-teaming-internet-connections/
Yes you can. See UbuntuBonding.