If I go to a travel agent, then can they get me a better connection than online travel booking sites like Expedia?
If you have a good travel agent they are likely to think about options you have not thought about yourself, know alternatives for routes from your home town and they may well know more about your destination than you do yourself. And they might have more knowledge on which companies are likely to overbook accommodation to the point where many guests will have to accept alternative options, which companies show their few good rooms online and have a lot of much worse rooms for those who show up late at night.
And when you build up a relationship with a travel agent, they get to know what you want and accept and which alternatives they do not need to offer, which can be time and money savers in the future.
But a travel agency that does not work for you is worse than booking on internet yourself.
I have been blessed by a very good travel agency for years, now they stopped I struggle to find one that is up to my expectations, so far all have failed.
It is possible that the travel agent may have more options - but it depends on too many factors:
The sector you are flying and the date of your travels (if it's during a busy holiday season and between a popular route - say New York - London, then travel agents may reserve blocks in advance)
The airline you are flying on.
Your itinerary - especially if you are not flying on a code-share flight.
However, there is no guaranteed yes or no answer; but since most travel agents are willing to quote you over the phone, it is just easier to ask.
Is it possible? Yes.
Is it likely you will find a better deal? No.
Today, there are very few ways Travel Agents can offer a better deal. Examples would be promotional fares available only to certain agents, consolidator fares, commission kickbacks or fraud.