No. Most cards have several LEDs. Some which indicate an established link, some which indicate data transmission.
If your cards have no link, e,g, due to a broken cable, or because you use a plain Ethernet (not a crosscable) between olders network interfaces without MDI/MDX then you will not get a link.
Your card could also be one with only a transmission LED. In which case establishing merely a link but not transmitting anything would not cause it to light up.
In your case I would start with:
- Do things work as expected, just no LED. (In which case see above two reasons).
- If it does not work, do a have a proper cable (cross cable)
- Does my cable work with other hardware? (not only right type, but is it also unbroken).