Tim,
The answer is: No
I'm not sure what tube(s) that old HXL 1 uses (my memory of old Hammarlund gear is limited).....BUT, the answer here is one that applies to most all amps / transceivers.....
Your transceiver ("exciter") "sees" the input of the amp as its "load" when the amp is ON and in the "operate" position.....NOT the antenna......so the antenna match is actually irrelavent......
It is the "INPUT impedance" of the HXL 1 that determines what load is seen by your transceiver, and hence what swr you measure _at the tranceiver_.....
What is the input impedance of the HXL 1

?
I'm not sure, but since it is an older amp, it surely was NOT designed to provide a "50 ohm resistive load" at the "input" of the amp, across the bands......as the "exciters" of the day were able to load up into a wide impedance variation and did need to be "tuned up" after changing bands or large QSY's (vacuum tube final amps w/ broad tuning ranges)....
If your present transceiver does not like the match it is getting, and it is "folding back" its power output because of this poor swr, then you may be able to use your rig's internal antenna tuner (if it has one), to quickly and easily provide you with a solution.....
Simply allow the internal tuner to tune into the amp, while transmitting with the amp ON and in the OPERATE position.....you'll get a good match and be able to drive the amp just fine....
Since most modern solid-state final amateur tranceivers use transistors that have little margin / tolerance for higher voltages that can be produced by high reflected power (high swr), these manufactures design in an "swr power fold back" circuit that reduces the transceiver's power output when subjected to high swr.......
This is why most "modern KW hf amps" have "tuned inputs" or are designed to provide a fairly good input match across all of the amateur HF bands......
(some of the "grid-driven" tetrode amps, many using the "russian" 4cx800, actually use a 50 ohm load resistor on the input to act as an input attentuator, and as a result it also gives them a fairly good input match to most radios....)
I hope this helps explain the situation.....
BTW, if you are not experiencing any significant "swr power fold back", then I wouldn't give it any other thought....
BUT, if are experiencing a substancial power reduction, and your transceiver does NOT have an internal tuner.....your options are limited to:
1) adding some input tuning circuits to your HXL 1.
(or maybe a simple modification to the amp's input circuit???)
2) adding an "antenna tuner" between your rig and amp.
3) simply bypassing or adjusting your rigs "swr fold back crcuit" to allow you to properly drive the amp....
While, I'd recommend #3, only if your rig is actually capable of handling it(don't know what rig you are using).....as long as your swr INTO your amp is < 3:1, this is a possibilty.....and if it's < 2:1, I can't forsee any problem at all......
BUT the choice is yours!!
Good luck.
73,
John, KA4WJA