There was a really good map of the distribution of Y-DNA in the world but I can't find it in very good quality atm, in the meantime you'll just have to make do with this map. The haplotype associated with Yamnaya migrations (the peoples from the Pontic-Caspian Steppes who supposedly spoke PIE) is called R1a, and is particularly prevalent in Eastern Europe, but also to some degree in Northern India. But it's much less present in Western Europe, and most of the population of the UK for instance is genetically descended from the original inhabitants who migrated into Britain from Spain after the ice age. So to answer your question, yes and no.

The Y-DNA map linked by /u/Holytriplem is out-dated. There was a major paper published in Nature on the whole genomic contribution of Indo-Europeans to the European population back in March.

Here's the paper. As you can see in this chart, the Indo-European contribution to the Basque sample is actually higher than the generic Spanish sample, and especially higher than the Indo-European-speaking Sardinian sample.

So it's just a mixed picture. In some Indo-European-speaking populations, the Indo-European genetic contribution is large. In others, it isn't.

hi! your first two questions about genetics would be a better fit for /r/AskScience (Biology category); it would be worth x-posting this question