As far as I know, it does indeed make no difference, unless the defending force is extremely small (a few million, rather than billion). I've had invasions where I have taken no losses though I should have lost a few mil. With the enemy population over a certain threshold (I don't know the cut off point), overwhelming them with numbers makes no difference in your losses.

Going back to he original question versus the responce what. I would ask them have U ever played a game in the middle of a war and forgot to save and replayed part of the game again  I have. I've seen what has happened when  U invade with massive troop transports advanced troop transports attacking with 3 transports in a fleet or 1 multiple troop mods on 1 ship I would also ask them a question if they pay attention to the invasion screen instead of watching the stats while they r going on while u r attacking or defending My guess their answer to this question just judging from their responce is no because one of the factors is how much troops or population u have the things I mention above will affect your chances this will also I don't recommend using weapons that will lower planet quality unless your someone who don't build structures unless u have advanced toxic world colonization the same thing is dido as for structures they r rebuildable propagamda if u have the money it will help mini soldiers r good too. The more troops the better even if u don't sucessfully invade I've been on the defending end against the iconians and losing for 2 days if your population drops to low on your capital or to many planets this will hurt your production and your funds either way I've seen 3 billion take exactly the same planet at the same time 1 billion couldn't take because forgetting to save more troops the better but u have to remember that is only 1 of the factors u can increase your chances by starting at the right time with the odds how much tech u or they have propaganda or another attack methid will help and if u are Korath and have spore ships everyone dies on the defending planet without loss of lives for the Korath but remember if u don't have advanced toxic world colonization u only have half production. This is something I have tried more troops or higher population depending wether u r attacking or defending the better