To say that a "traditional" assassin would be useless in modern warfare is quite uneducated. An assassin, with what we know today, uses tactics, not weapons, to kill their target. Subterfuge, infiltration, stealth: these are the tools of a true assassin. The murder weapon would really depend on how close you can get to the target.
Why do I mention that? Well, when the intent is to kill someone, the closer you are to the target, the better. It ensures less foul ups. Sniper rifles are all nice and shiney, but there are sometimes just too many variable to consider. A combat knife or garrote are much more accurate and offer less hassle than studying how to shoot a rifle at 2 clicks away, simply because it depends on a skill set an assassin must already know, the art of deception.
These skills are best seen in an assassin know far and wide known as the ninja. I remember watching a documentry on the ninja on the Discovery Channel one evening and it essentially posed this same question. Could ninjutsu be just as effective today as it was back in feudal Japan. The fact is: yes, it is. A moderm day ninja master was able to, under the rules of "No one is allowed beyond this point" after the V.I.P. was considered in danger, play himself off as one of the technical staff and gain the trust of the two bodyguards by cleaning hidden camera lenses, bringing them catered food, etc. and effectively assassinate the V.I.P. at melee range over the course of about 8 hours! It was even stated by various special ops infantry, there to give their two cents and watch the demonstration, use tactics very similar to the ninja master to get close to their targets for mid-range rifle combat.
Now, take the situation above and relate it to an embasy where no immediate threat is present. Take all those skills an assassin must know in the ways of deception, subterfuge and stealth. To say that a true assassin couldn't just implant himself into this embasy, gain access to the V.I.P., stab his neck with a combat knife (which renders your vocal chordes useless and your time extremely limited because of massive bleeding) and then walk out after a quick change of clothes (planted earlier) is not unrealistic. SNAFUs in guard change, guard duty, etc. are probably common place. Get the guard at that time to really need to take a piss, offer to replace him for the five minutes, get your job done, walk off, and have the body discovered several hours later would probably be a snap for someone trained well enough.
In conclusion: it is possible, but I doubt it would be terribly practicle, simply because of time contraints, resources/connections needed, and the immense amount of training.
