No. The catch-up contribution is an annual amount. It cannot be taken separately on each account. Per IRS Publication 969:
Additional contribution.
If you are an eligible individual who is age 55 or older at the end of your tax year, your contribution limit is increased by $1,000. For example, if you have self-only coverage, you can contribute up to $4,500 (the contribution limit for self-only coverage ($3,500) plus the additional contribution of $1,000)... If you have more than one HSA in 2019, your total contributions to all the HSAs can’t be more than the limits discussed earlier.
IRS Publication 969
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