Even legitimate children cannot 'just' make a claim on a parents written will, unless they can show that the parent was paying for their upkeep, eg. an able bodied 22 year old would have no claim if he was not shown in the will, the same applies to illegitimate children. Although anyone can challenge a will, it is expensive and the proof and reasoning would have to be good. Under 18, if the parent was paying towards the upkeep of the child, legitimate or illigitimate, money to continue the upkeep until the 18th birthday would have to be put aside, normally in a trust fund.
If Harry was killed in Iraq how could he acknowledge paternity of the unborn child? How would they word the will to ensure the unborn child would be entitled to anything from Harry's estate. It would have to be along the lines of "My girlfriend Chelsy Davy is I believe carrying my unborn child and if after DNA tests this is confirmed..... I wish the child to benefit from my estate in the sum of...... Then you have the problem of what if it is twins!
I am reasonably certain that Harry and whoever he marries, will wait until after the wedding before bringing any child into the world.