Yes, there is always an electric field around a battery, even when nothing is connected to the battery.
However, if there isn't a current flowing, the electric field doesn't have much of an effect, because no energy is being expended doing anything interesting according to Watt's law, $P=VI$.
The field does exert a Lorentz force $F=qE$ on a charged object near the battery, but the force isn't very large because the field strength $E$ isn't very large given a typical battery's voltage and distance between the terminals. For example, the electric field produced by a battery is much weaker than the field involved in everyday static electricity effects, such as when you rub your feet on the carpet when the air is dry. Those everyday static electricity effects involve potential differences of thousands of volts, much larger than the 9 volts or less of a typical battery.
Another way to look at how weak the electric field is around a battery is to compare it to how strong the field would need to be in order to cause a spark to jump between the terminals. The field around a battery in reality is complicated due to the complicated geometry involved, but it's helpful in making a rough estimate to consider that in a uniform electric field, such as between two large charged parallel plates, the magnitude of the electric field is $E=V/d$, where $V$ is the voltage between the plates, and $d$ is the distance between them. The breakdown field strength of air is about $3MV/m$, which means that in order to get a spark to go between the terminals of a 9V battery, the terminals would have to be only about $3\mu m$ apart, about a thousand times closer together than they really are. Put another way, the electric field between the terminals is about a thousand times too weak to produce a spark between the terminals.