Yes. You can set ICQ to auto-accept files from a friend on your contact list.
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From the Main menu choose Options.
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In the Options window Customization tab in the left pane, click the Messages&Files option.
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In the right pane, click the Set per contact link.

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From the Don't auto-accept pane select the friend for which you want to automatically accept files and click the left pointing arrows button; The name now appears in the Auto-accept pane.

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Click OK to close the Set per contact window, then click OK to close the Options window.