Even with our current medical technology 'death' is more of a process than a state. Someone fished out of a cold river (having been submerged for up to 45 minutes) can often be revived with no serious problems. People who've been 'dead' for several minutes have been resuscitated with no ill effects, etc.
Thus, we have to consider what it actually means to be 'dead'. Death is, biologically speaking, a cessation of the functions of life. Let's make this as strict as possible and say that it includes a cessation of brain activity and biological functions. Let's also put a time on it - beyond a few minutes, a hospital generally can't save someone who is dead. Prior to that, resuscitation is (sometimes) possible.
The longest time I can find reported for resuscitation is about 30 minutes (a child submerged in cold water). Let's extend that to account for alien tech. Let's say that 'magic alien tech' can extend that by a factor of 50 (1500 minutes, or 25 hours).
So, for the purposes of general sci-fi (without explicitly stated medical tech that gives a longer or shorter duration) let's say any person can be revived within 25 hours.
Using this general measuring stick, Daniel Jackson HAS died. When he ascended, his body died. His 'essence' or 'soul' or 'personality' or SOMETHING survived, true, but he met every medical definition of dead. Later, when he visited the restaurant with Oma, he did it again. His body was destroyed, and he had no detectable life signs. A part of him lived on, but isn't that what the 'soul' or 'essence' is supposed to do after death?
So we can confidently state that Daniel has died 2 times, even under the loosest sci-fi definition of death.
More specifically to Stargate, Daniel died during the failed ambush of Apophis. The Nox certainly considered him dead, just as they considered the child who was killed later in the episode to be dead. They may have been able to reverse the process, but they did know there was an upper limit to their ability to do so (which was considerably less than the 25 hour estimate above). Thus, we can see Daniel has died at least 3 times by the rules of Stargate.
Finally, consider the movie. Daniel Jackson dies from a staff blast, only to be revived by Ra. Daniel certainly thinks he died at least. He said as much himself.
Thus, under the definition in common use today (such as doctors use when discussing patients who flatline) Daniel has died many times.
TL;DR: Yes, Daniel has died. How many times he's died, however, depends upon your definition of 'dead'.