Don't think it's him
The Thomas Ainsworth of the profile was born in Jan 1812 in Manchester.
The profile states "There was a Thomas Ainsworth on board the Camden in 1833, provided Certificate of Freedom in 1844 and Royal Pardon in 1847 which may be the same"
Unfortunately, according to his Certificate of Freedom, the Thomas Ainsworth, convicted at Warwick and arrived on the Camden in 1833 was born in 1817 and was a native of Birmingham. (He stole a watch)
New South Wales Government. Butts of Certificates of Freedom. NRS 1165, 1166, 1167, 12208, 12210, reels 601, 602, 604, 982-1027. State Records Authority of New South Wales, Kingswood, New South Wales [accessed ancestry.uk]
The problem is that there doesn't seem to be another close candidate. (unless he didn't arrive until 10 years later than stated)