The quick answer - no.
This is a honey produced by bees exposed to pollen from the Manuka tree, mostly in New Zealand and Australia. It sold at incredibly high prices for honey - as much as £50 or more for a small jar.
Unfortunately, this is a classic case of assuming something that has a topical benefit - if you use it externally - will have a benefit if consumed. And as is usually the case, there is no link.
Honey in general has a mild anti-bacterial action (as do many substances - washing up liquid, for instance) - and there is reasonable evidence that Manuka honey is amongst the best at this. So applied appropriately to a wound (and I'm not recommending just slapping honey on), it can in principle have a positive effect (though there are many other, cheaper and more effective anti-bacterial agents).
When you eat it, though, it has no impact on your immune system. As discussed in Science for Life:
And in this case there is no evidence that the honey will be anything more than an incredibly expensive sweetener, adding unnecessary sugar to your diet. See the Cochrane report for details on use of honey in treating wounds.Your immune system is not a single part of your body but rather a vast network comprising physical barriers like your skin, white blood cells, various different organs and a whole range of complex chemicals with literally thousands of different roles. ‘Boosting’ it by simply eating something is a bit like hoping to redecorate your house by throwing a capsule of paint at the wall.