Aishwarya Rai’s success has next to nothing to do with her marriage with Abhishek Bachchan. Infact I would suggest the opposite. Her stardom was adversely effected because of her marriage. In fact even Abhishek Bachchan’s career dwindled after marriage.
Aishwarya Rai was a popular model, winner of Miss World pageant and then transitioned into cinema with National award winning film Iruvar. She has since then achieved success with films like Ham Dil De Chuke Sanam, Taal, Devdas, Mohabbatein, Dhoom 2 etc. She also won Filmfare awards for HDDCS and Devdas. Not to forget she did Hollywood and crossover films like Bride and Prejudice, The Ministry of Spice etc. None of this was related to Bachchan family. In fact with Abhishek she did utter flops like Dhai Akshar Prem ke, Kuch na Kaho, Umrao Jaan etc. They did Dhoom 2 but they were not paired together and the film was a Blockbuster. They also did Guru together which was their best film together, not to forget their dance number Kajrare from Bunty aur Babli. All this happened before their marriage.
Now after marriage, Aishwarya did Sarkar Raj with Abhishek and Amitabh which did below average business. In 2008 she had one major National award winning hit Jodha Akbar but after that she had
Pink of Panther 2 - Disaster
The Legion- Disaster
Action Replay- Flop
Enthiran/Robot - Blockbuster
Ravan- Flop
Guzarish- Flop
(After this she took a long sabbatical from films for 5 years. Since then she has been on and off from films)
Jazbaa her comeback film- Flop
Sarbjit- Flop
Ae Dil hai Mushil- Hit
Fanney Khan- Disaster
PS-1 - Blockbuster
PS-2 - Hit
(None of her hits apart from Jodha Akbar post marriage were solo hits)
Abhishek Bachchan has even worse record post marriage
Sarkar Raj- Below Average
Drona- Disaster
Dostana- Above Average
Paa- Semi Hit
Delhi 6- Flop
Raavan- Flop
Khelein ham Jee Jaan se- Disaster
Game- Disaster
Dum Maaro Dum- Flop
Players - Flop
Bol Bachchan - Hit
Dhoom 3- All Time Blockbuster
Happy New Year- Superhit
Housefull 3- Hit
All is well- Disaster
Manmarziyan- Flop
(Since then Abhishek Bachchan has 10 releases but only 3 released in theatres rest all were OTT releases where he found new found appreciation and acclaim but his films in theatres didn't do well even when they were accalimed like I want to Talk, Ghoomar etc.)
So to say that Aishwarya was benefited from Bachchan surname is quite stupid. She made her career way before any association with Bacchans. Also she is one of the rare actresses to work considerably in Hollywood with 5 Hollywood or crossover films apart from regular visit to Cannes.