Indeed, such a declaration would've thrown down the gantlet to the RN and challenge its very supremacy in American waters. I can't see the RN tucking tail and caving on this issue especially when threatened with force.
If a naval conflict breaks out in 1807-1808, I think the results would favor the USN much as they did in 1812 OTL probably even more so. Nationalist fervor would undoubtedly lead to a large naval build up on the great lakes.
The main question of the war expanding would rest on the British deciding whether the 5,000 or so impressed American are worth the price of redeploying additional forces to North America, especially when considering that in OTL over 1,000 impressed sailors preferred to spend the War of 1812 in British prisons rather than fight their own country.
Why in God's name would the USN, even IF it possessed 8-12 Ships of the Line & 13 frigates (which would have bankrupted the U.S. government, the fleet as it was consumed an average of 20% of the U.S. TOTAL budget from 1800 - 1810, even with the 1802 anomaly), want to throw down the gauntlet before the Royal Navy?
The British, in 1805, had 106 ships rate 74 guns or higher, and additional 16 razeed 74's rated 44 to 50 guns (+ 19 in ordinary), 133 frigates (+ 96 in ordinary), and 400+ sloops of war. In addition, in 1805, the Royal navy had two 120 gun, three 100 gun, one 98 gun, and twenty 74 gun Ships of the Line under construction. The USN fleet that has been proposed would not even be a decent squadron by comparision, not against the naval powers of the day (The French/Spanish fleet at Trafalager numbered 33 ships 74 or higher, Nelson, commanded 27).
How did the War of 1812 conditions favor the U.S.? The USN LOST the Naval phase of the War of 1812. Despite the rather inspiring victories of
Constitution and other frigates the USN was outmatched, outnumbered and out gunned. Even the sidshow on the Lakes was, like the war itself, at best, a draw.
The USN had some very nice one on one victories when frigates of the USN & RN engaged (as noted, the American Frigates were more like razeed 74's than actual frigates) but the war ended with virtually the entire American Navy bottled up in one port or another by RN blockade or captured (only
Constitution was at sea among the frigates, and she had been blockaded for months before breaking out). Specifically:
USS Adams Blockaded 1812 to 1/18/1814. Burned to prevent capture 3/9/1814.
USS Chesapeake Captured 6/1/1813
USS Congress Blockaded 12/14/1813
USS Constellation In Ordinary at start of war. Sailed in December 1812; Blockaded January 1813
USS Constitution Blockaded on several occasions. Escaped, was at sea when war ended.
USS Essex Captured by RN 3/28/1814
USS John Adams Blockaded 1812 to April 1814; released under flag of truce carrying American diplomats to Peace Conference
USS New York In ordinary at start of war Burned 8/24/1814
USS President Blockaded February 1814 to 1/15/1815; Captured by British 1/16/1815
USS United States Blockaded 6/1/1813
The United States in 1800, or 1810, or 1820, or 1830, etc. was no match for the Royal Navy, a condition that remained true until the 1920's (save 1862-1865, and then only if the RN was obliging enough to close to 10 miles or less off the U.S. coast). The British Empire was 1) Rich, 2) Very Rich, 3) Filthy Rich & 4) An EMPIRE (and a rich one at that)

. The United States, prior to 1880 or so was anything but rich; look at the Budget for any year during the period, you will notice that there is IS NO MONEY. Even after 1880, it wasn't until 1913, with the introduction of the Income Tax (BOO! HISS!!

) that the American government had sufficient funds to build a serious, balanced fleet (the WW I American fleet was terrific, as long as you only counted battleships, if you added in cruisers and destroyers, she came up a bit short.)
In the 1800s England ruled the waves, just that simple. It galls my hyper-patriotic American self to say it, but it's true.