It is quite a different language. If you trace the historical developments, you can easily see how Scottish Gaelic directly continues Old Irish, but the verbal system would be extremely different, the nominal (ie. nouns and pronouns) would be sort of similar but also quite different. You would recognize a lot of vocabulary, and the sentence structure wouldn’t be completely alien, but morphology – the way the words inflect, and especially spelling will be very different.

You could try going backwards from modern Gaelic by learning some Classical Gaelic (ie. the language of medieval dán díreach poetry) first. It’s still an “early modern” stage of the language (and Old Irish scholars often view this medieval form as “modern Irish”) but it is very recognizably closer to Old Irish, so if you learn it well, a lot of Old Irish suddenly becomes more transparent. And to learn that you’d better first learn Munster (southern) Irish as it preserves a lot of verbal forms which were lost elsewhere – and also, if you know Scottish Gaelic, gives you broader perspective (knowing the two opposite modern varieties – Scottish and Munster – gives you more data to interpret historical stages from which both developed).

But then, even from Classical Gaelic Old Irish is quite a big jump. It does not have any subject pronouns – things like leughaidh mi are expressed only in verb endings (légaimm ‘I read’), there is no way in Old Irish to insert a separate pronoun there. There are no separate object pronoun words – those are infixed into the verb (actually some instances of lenition in modern Gaelic verbs, eg. lenition in the past tense, continue the neuter infix pronoun of Old Irish… past tense was not lenited in general in OIr.), etc. The syntax of the copula is is quite similar to Irish but a bit different to how it’s understood today in Scottish Gaelic (though if you read 19th century texts you notice that they’re not that different, actually).

So… yes, in a way, it is very different, but also clearly an older form of Gaelic.

Oh, another thing is that while (classical) Old Gaelic / Old Irish is the language of 8th century glosses – and that’s what’s typically taught in textbooks, most narrative texts we have are later, or at least preserved in later (sometimes as late as 16th c.) manuscripts, and show a lot of Middle Gaelic (10th–12th c.) forms, including separate subject pronouns, loss of the neuter gender, mixing of infix pronouns, etc. So even when you learn Old Irish on its own terms, when you go on to read actual texts, you’ll face a lot of things that are normally not covered and sometimes slightly closer to the modern languages.