If it's really only $30 to add the extra day, I don't see a lot to lose. OP stated they would get in Monday afternoon. Guess it depends what time. If they don't arrive until 5pm and have been in the car all day, I'd be inclined to skip it too. If they leave early in the morning, arrive at 2pm, and most of the passengers slept a lot for the drive down, then without a doubt I'd go to the parks.
For us, we typically drive down after I get off work. It's a 7-8 hour drive and we usually leave around 4 or 5pm, so it's a non-issue for us...we don't arrive until midnight. When we used to live in PA, we had to fly down. We'd get an early am flight, such as 6:30am. We'd be at the parks by 10:00am. We were all tired and didn't make it a late night, but we still went to the park.
It also depends on how long your trip is. If it's only a few days, I'd take advantage of every possible second. If it's a really long trip, not as worried about it. OP also mentioned making their "first trip". If I'm a first time WDW visitor, I'd be in the parks whenever possible.