Suppose I install Ubuntu on a Virtual Box, will I be able to use my Windows Internet connection, which is connected through a wireless device that Ubuntu is unable to detect?
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VirtualBox presents to the Guest an equivalent of a fixed ethernet hardware device. Remember, a virtual guest does not have to rely on the underlying host hardware. Therefore, to the virtual Ubuntu, it thinks it is seeing a fixed ethernet cable connection.
The default for VirtualBox is to provide a virtual network capability, which connects the networking traffic from one device to another.
N.B. this shouldnt be confused with the Windows Bridging Network Adapter which is another thing entirely.
By default, the active Host network (your windows wireless in your case) is linked to the virtual hardware device through what is termed Network Addressed Translation (NAT). This is just a capability to allow two devices (in this case Windows and the Virtual Ubuntu) to share the same IP address.
Thus, assuming that your windows networking is correctly setup and you've haven't fiddled too much with the virtual box ubuntu guest settings, your virtual Ubuntu guest will use your Windows wireless network without any further tweaks.