Not especially.
The Imperium's "average" TL is not an easy thing to define.
The average imperial world may be TL11-12 or so, but the average imperial citizen lives on a multi-billion-person TL14-15 world (because the population of entire subsectors worth of thousand-to-million inhabitant worlds can vanish into one big core world). Equally, whilst system and subsector fleets have wildly varying tech levels, the Imperial Navy is pretty solidly nailed to TL14+.
The exact TL doesn't matter any more than the exact displacement of his ships; essentially Imperial Navy dreadnought BATRON formations can waste his ships, but will take extremely expensive losses doing so, because whilst he has a massive tech advantage, he is at a massive tonnage disadvantage, and has extremely limited options to make good damage or losses.
I like the idea that, in order throw off pursuit, he just had his flagships computer randomly pick a less advanced galaxy that was at least 440 years time at Jump 6 from his own races territory, ours was the 1 randomly picked, pressed fhe button to do it and hoped for the best
Right. So it's "run like hell" then, and he doesn't start with any contacts or specific resources that he didn't bring with him.
Equally, that means no-one will specifically know who he is, or that he's a pirate. Most likely, you're going to see a bidding war, drifting discretely in and out of actual war, between various polities trying to get their hands on his services, ships, personnel and databases.
Discovering that there's a massive super-empire out there is disconcerting, but there is basically naff all that the Imperium or consulate could do about, so it'll be largely ignored in favour of more immediate problems; the pirate's ships and data either needs to be in their hands only, in their hands as well as anyone elses, or in shattered wreckage that no-one gets (and dreadnoughts would be moved up to ensure this). This is potentially a 'Cuban missile crisis' negotiation.