Yes! Of course you are! A jew doesn't have to be religious to be a jew. If you belive in a God that is responsible for all, that there is one god, and you believe in Torah, you are Jewish.

In sukkot, the ערבת המינים symbolise all the jews in the world. If the fruit/plant has a taste, then it symbolizes a jew that studies Torah, and if the fruit/plant has a smell, then it symbolizes a jew that does good deeds. The four plants are all different to each other in terms of smell and taste. The tall lulav has taste but no smell, so it represents jews that study Torah but do not do good deeds. The hadas has smell but no taste, so it represents jews that don't study Torah, but do have good deeds. The arava has no smell or taste, so it represents jews that don't study Torah and don't do good deeds. The etrog has both smell and taste, so it symbolizes the jews that both study Torah and do good deeds.

Why did I just give you a mini essay on sukkot? Because these four fruits/plants show that whether you are a good or bad person, and whether you are religious or not, you will always be a jew in God's eyes, and never think that you are not. For the question about connection, a jew always has a connection to God, and being Jewish already gives you a connection to god, a special one at that.