Generally speaking, unless you plan to live in a remote location where there is no grid available, yes you will maintain your relationship with your local power utility.
The type of solar PV system you are likely to receive is known as a grid-tied solar system. This means that your solar system will operate in tandem with your local power utility. The utility grid acts to solve the timing discrepancy between the amount of energy you are consuming vs. the amount your solar system is producing at a given moment.
For example: if during the day you produce more power than you consume at a given moment, the excess power is pumped onto the grid and your utility meter spins backwards. Likewise, during the night you will consume more than you produce (solar panels do not produce energy in the absence of sun light), and that power will come from power grid.
At the end of the utility billing cycle, you will be liable for energy you have used from the grid minus energy you returned to the grid. If you have produced more energy than you have used on a given month, you will receive a credit on your next month’s billing cycle.