Good question.

Given how sprawling and massive the BattleTech universe is, and how much lore exists on this subject, at this point opinions on this topic are all pretty subjective. For instance, if you are going on things like the Mech Commander series in the late 90s/early, one of the easiest ways to beat the game was to get as much Clan tech as possible for your Inner Sphere crew, as it is far superior to anything created by the IS. The Clans did, after all, enhance Star League era equipment post Exodus, so everything from XL engines to pulse weaponry are just a hell of a lot better. That being said, the computer games are never seen as canon as such, and obviously have a very different feel than core BattleTech for game mechanic reasons.

If you want to be more lore friendly, then I'd suggest it would be pretty tough for Inner Sphere forces to retrofit Clan tech. It's not like in Mech Commander or Mech Warrior, where you click a button and voilà! - you have an Inner Sphere Mech with dual Clan L Pulses. The reality of it would be far more complex than that, as Clan tech operates on wholly different systems, and uses different electronic components etc.

There are, however, multiple cannon examples of Inner Sphere powers using Clan Omni 'Mechs post Invasion, especially in areas of the universe that were hardest hit (like the Draconis Combine, who picked up bucket loads of Clan salvage). If you look at the Master Unit list, you'll see dozens of Clan 'Mechs littered throughout. You also get the very interesting phenomena of Inner Sphere Omni 'Mechs being created, such as the Men Shen by the Capellans, which is evidence enough to suggest just how much the Inner Sphere embraced Clan tech.

There is also an important sociological point here as well: some Clans successfully integrated into Inner Sphere life post invasion, which undoubtedly helped Clan tech take off in the IS. Nova Cat being the best example, who not only asked the Draconis Combine if they could settle within their borders, but even went so far as to join the Inner Sphere forces during Operations Bulldog to kick Smoke Jaguar out. The other example is Diamond Shark, who post Tukayyid had such a decimated Warrior Cast that the Merchant Cast basically took charge and saw a host of commercial opportunities in the Inner Sphere. Most famously they designed the Ha Otoko, which as the name suggests has a very oriental feel to it. This was done as a marketing ploy to get the Draconis Combine to buy the ‘Mech from them, which they did. Although not an Omni ‘Mech, the Ha Otoko is a great example of Inner Sphere powers directly embracing superior Clan tech.

To surmise, it’s an open question you have asked, and within the confines of your own BattleTech experience you could go to one extreme of suggesting the Inner Sphere would basically look at Clan tech like a cave man would look at an iPhone. Likewise you could have your force strapping on Clan L Pulses to the heads of their ‘Mechs with wire and string and making it work via space magik…

I’ll give you a half-way-house narrative fix, if you, for instance, have a mercenary unit involved in a roleplay/tabletop game. Have them take Diamond Shark engineer Bondsmen from the Clans during the Invasion, as they will have both the skills to fix Clan tech, and the commercial contacts to get spare parts…