This is what RAW says.
"INVISIBLE
• An invisible creature is impossible to see without the aid of magic or a special sense. For the purpose of hiding, the creature is heavily obscured. The creature's location can be detected by any noise it makes or any tracks it leaves.
• Attack rolls against the creature have disadvantage, and the creature's attack rolls have advantage."
If you are not invisible, you do not get those bullet points. If someone casts See Invisibility, you are no longer invisible to that person per the RAW of See Invisible. Therefore, by RAW you do not get those bullet points since you are not invisible to get them. To someone else you would still be invisible and get the benefit of the condition.
You have to be, you know, INVISIBLE to get the benefits of the INVISIBLE condition. VISIBLE people do not get it. See Invisibility makes you VISIBLE by RAW.