Can you be a Transgender while being a regular gender?

Yes, since so many define the term transgender in so many different ways. If you use it to refer to those who feel uncomfortable in society's gender roles, then you can have this discomfort while living as an ordinary man or a woman.

Now, it is possible to live in such a way where one is gender variant but who is within an acceptable amount of variance. For instance, tomboys are girls who like to do a lot of things traditionally done by boys, and the majority still grow up to be heterosexual and are accepted just fine among other women. In more modern times, there are metrosexuals, and these are guys who tend to care for their appearance more than other men, who might be "softer" in some ways, but may actually be heterosexual and content to be men.

If you consider transgender as something immutable, then a comparison could be made to race. Back during Jim Crow laws, there were African-Americans who were so light-skinned that they could get by with calling themselves white. That was illegal, but it did happen, and you cannot blame anyone for not wanting to be different from the majority if being different means persecution. So then, using this model, there could be a lot of transgender people passing as the gender that correlates with their sex organs.