Absolutely!
Here's a tip on planting carrots seeds, which are tiny -- pat down the soil and make narrow, but shallow trenches about 12 inches apart.
Mix your carrot seed with sand to make it easier to sow in the trenches, pop in a radish seed every six inches. Cover lightly. Water.
The radishes will pop up quickly and let you know where your carrots are. Carrots take anywhere from 60-80 days but radishes will be up in a month. Try to get an early maturing carrot because they won't like the heat. In the fall, you can sow some overwintering carrots that just get sweeter after the first frosts.
For peas -- get Sugar Snap or Super Sugar Snap, available pretty much anywhere. Plant in a trench row about one inch apart, no further than that. When peas grow up closely, they help support each other.
You will need a trellis system for peas. Bamboo stakes work great.