All children are different but yes it's normal for a 6 year old to be emotional.
It's normal to be pretty emotional at any age as well and usually though your 6 year old will stop being so emotional as they age.
At 6 years old it's still a learning process for them and can be hard for the 6 year old to control their emotions like an older child would be able to do.
So a 6 year old may cry more at little petty things than an older child would do and you can also expect tantrums out of 6 year old and even 7 year old child and be prepared for the tantrums in public as well.
But the good news is that tantrums in children get less and less as they get older.
Yes it's normal for a 6 year old to cry a lot and even in public some 6 year old children will cry a lot and throw tantrums especially in a store when they cannot get what they want.
I've seen 6 year old kids in stores that wanted things and the parents could not or would not buy what they wanted so they would cry and throw a tantrum in the store.
I saw one mother spank her 6 year old boy in the store over a tantrum and it stopped the tantrum right then and there although he still had tears in his eyes he stopped throwing the tantrum and was trying to stop crying.
All children are different and some 6 year old children may cry more than others and even I cried a lot when I was 6 years old.
But when a child gets above 6 years old they tend to cry less and by the time they get to 8 or 9 years old they will rarely if ever have a tantrum and cry in public in the store as they learn to control their emotions and learn that crying won't get them what they want.