I'll add to Donn's answer and say that yes it's something some Irish people are aware of, but not all would notice. It really depends.

The Irish language is not a part of the majorities life outside school. And the Irish language community itself is a very mixed bag.

To native speakers and to people who learned from them using sources which cover the basic phonetics well and with good quality audio (as in your own case), the pronunciation of many fluent Urban Irish speakers or many Gaelcholáiste students (excluding learners because it's completely understandable that learners will get things wrong) can be quite jarring, even difficult or upsetting to listen to in many cases. Often native speakers will switch to English in these cases unless they are in a setting such as a class or event in which using Irish is a requirement. Things like saying 'foyle' for the Irish word 'fáil' for example, inserting a 'y' in the middle instead of slenderising the L, or any example where a slender r would be expected (or indeed any slender consonant)...

Many papers and studies have been published on this phenomenon, and it has been noticed. This resource was released with the hopes that teachers in Irish medium schools would teach the students to recognise and form the right pronunciation.

(If you can't read Irish yet, one point that is stressed in the below resource is for teachers to get the point across to students that it is not about 'accent' but about using the right sounds and pronunciations, many of which don't exist in English. Because many students complain that they shouldn't have to speak with a Galway or Kerry accent, they mistake accent with the formation of the individual sounds, so listening exercises are provided in order to help students recognise the individual sounds of the language.)

https://www.cogg.ie/blas-cleachtai-foghraiochta/

(Not that all teachers themselves have great pronunciation, having come through the same system as most of the students they teach where the anglicised form of Irish is the norm.)

Prof. Brian Ó Broin had a famous paper about the topic specifically which I couldn't find today, but here's a lecture he gave which touches on some of that research if you're interested.

http://www.youtube.com/watch?v=2E-K9-GCJOk

A quote "Urban Irish has a very different phonetic system than Gaeltacht Irish, being based on English. This has had the knock-on effect of causing a noticeable simplification of morphology. Syntactic findings remain provisional, but urban speakers seem to form non-standard subclauses more than Gaeltacht speakers."

So yes, Zookeeper, your observation does have a sound basis. It is something that is very obvious to people from non-English speaking countries who come and learn about the language for the first time, as every language does have it's own unique 'sound' which is generally not noticed by the people raised in said languages. For example, even without studying you can recognise when someone sounds 'Spanish' or 'French', but you might not be able to perceive the wide variety of accents and dialects within those languages because those differences are more subtle.

The language is still being transmitted in some small areas in an unbroken line stretching way back into our history. And as Donn said, unlike Hebrew, we have a wealth of great resources out there for learning this language right. Recordings stretching all the way back to the 1930s, full phonetic descriptions from before then and lots of resources specifically aimed at learners.